Solve 56000=(1+8.15%/12)^48-1/Ax8.15^9/12

$$56000 = \frac { ( 1 + \frac { 8.15 \% } { 12 } ) ^ { 48 } - 1 } { A x } \frac { 8.15 ^ { 9 } } { 12 }$$

Solve for A

$$A=\frac{7923847882002845181309439774188096657933984031059104771715715846022994889539694246601419107202130081496635193706518322056570891905319447467793401044266301017219312648055088717366862337231995751231313859223360300343383702500954469}{87434090370683579095849480698159468868987743401213122360860767265226752000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable A cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12Ax, the least common multiple of Ax,12.

$$672000Ax=12\left(\left(1+\frac{\frac{8.15}{100}}{12}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Expand \frac{8.15}{100} by multiplying both numerator and the denominator by 100.

$$672000Ax=12\left(\left(1+\frac{\frac{815}{10000}}{12}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Reduce the fraction \frac{815}{10000} to lowest terms by extracting and canceling out 5.

$$672000Ax=12\left(\left(1+\frac{\frac{163}{2000}}{12}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Express \frac{\frac{163}{2000}}{12} as a single fraction.

$$672000Ax=12\left(\left(1+\frac{163}{2000\times 12}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Multiply 2000 and 12 to get 24000.

$$672000Ax=12\left(\left(1+\frac{163}{24000}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Add 1 and \frac{163}{24000} to get \frac{24163}{24000}.

$$672000Ax=12\left(\left(\frac{24163}{24000}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Calculate \frac{24163}{24000} to the power of 48 and get \frac{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$672000Ax=12\left(\frac{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}-1\right)\times \frac{8.15^{9}}{12}$$

Subtract 1 from \frac{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$672000Ax=12\times \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{8.15^{9}}{12}$$

Multiply 12 and \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$672000Ax=\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{8.15^{9}}{12}$$

Calculate 8.15 to the power of 9 and get 158642110.417683091255859375.

$$672000Ax=\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{158642110.417683091255859375}{12}$$

Expand \frac{158642110.417683091255859375}{12} by multiplying both numerator and the denominator by 1000000000000000000.

$$672000Ax=\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{158642110417683091255859375}{12000000000000000000}$$

Reduce the fraction \frac{158642110417683091255859375}{12000000000000000000} to lowest terms by extracting and canceling out 1953125.

$$672000Ax=\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{81224760533853742723}{6144000000000}$$

Multiply \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} and \frac{81224760533853742723}{6144000000000} to get \frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$672000Ax=\frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

The equation is in standard form.

$$672000xA=\frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Divide both sides by 672000x.

$$\frac{672000xA}{672000x}=\frac{\frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{672000x}$$

Dividing by 672000x undoes the multiplication by 672000x.

$$A=\frac{\frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{672000x}$$

Divide \frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by 672000x.

$$A=\frac{7923847882002845181309439774188096657933984031059104771715715846022994889539694246601419107202130081496635193706518322056570891905319447467793401044266301017219312648055088717366862337231995751231313859223360300343383702500954469}{87434090370683579095849480698159468868987743401213122360860767265226752000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000x}$$

Variable A cannot be equal to 0.

$$A=\frac{7923847882002845181309439774188096657933984031059104771715715846022994889539694246601419107202130081496635193706518322056570891905319447467793401044266301017219312648055088717366862337231995751231313859223360300343383702500954469}{87434090370683579095849480698159468868987743401213122360860767265226752000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000x}\text{, }A\neq 0$$

Solve for x

$$x=\frac{7923847882002845181309439774188096657933984031059104771715715846022994889539694246601419107202130081496635193706518322056570891905319447467793401044266301017219312648055088717366862337231995751231313859223360300343383702500954469}{87434090370683579095849480698159468868987743401213122360860767265226752000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000A}$$

$$A\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12Ax, the least common multiple of Ax,12.

$$672000Ax=12\left(\left(1+\frac{\frac{8.15}{100}}{12}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Expand \frac{8.15}{100} by multiplying both numerator and the denominator by 100.

$$672000Ax=12\left(\left(1+\frac{\frac{815}{10000}}{12}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Reduce the fraction \frac{815}{10000} to lowest terms by extracting and canceling out 5.

$$672000Ax=12\left(\left(1+\frac{\frac{163}{2000}}{12}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Express \frac{\frac{163}{2000}}{12} as a single fraction.

$$672000Ax=12\left(\left(1+\frac{163}{2000\times 12}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Multiply 2000 and 12 to get 24000.

$$672000Ax=12\left(\left(1+\frac{163}{24000}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Add 1 and \frac{163}{24000} to get \frac{24163}{24000}.

$$672000Ax=12\left(\left(\frac{24163}{24000}\right)^{48}-1\right)\times \frac{8.15^{9}}{12}$$

Calculate \frac{24163}{24000} to the power of 48 and get \frac{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$672000Ax=12\left(\frac{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}-1\right)\times \frac{8.15^{9}}{12}$$

Subtract 1 from \frac{2461733224034489131407971643008605631536950216958917063797483878026072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$672000Ax=12\times \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{8.15^{9}}{12}$$

Multiply 12 and \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$672000Ax=\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{8.15^{9}}{12}$$

Calculate 8.15 to the power of 9 and get 158642110.417683091255859375.

$$672000Ax=\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{158642110.417683091255859375}{12}$$

Expand \frac{158642110.417683091255859375}{12} by multiplying both numerator and the denominator by 1000000000000000000.

$$672000Ax=\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{158642110417683091255859375}{12000000000000000000}$$

Reduce the fraction \frac{158642110417683091255859375}{12000000000000000000} to lowest terms by extracting and canceling out 1953125.

$$672000Ax=\frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{81224760533853742723}{6144000000000}$$

Multiply \frac{682882101584058241599836049377431541591724317682933942848981939850072491043172043844126391635094815618047986368653059782224959905213311538597542458094851760186145064917983616642101221177416883202195551108086721}{148237593537535907484011299469264507495435491606331926745708494848000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} and \frac{81224760533853742723}{6144000000000} to get \frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$672000Ax=\frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Divide both sides by 672000A.

$$\frac{672000Ax}{672000A}=\frac{\frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{672000A}$$

Dividing by 672000A undoes the multiplication by 672000A.

$$x=\frac{\frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{672000A}$$

Divide \frac{55466935174019916269166078419316676605537888217413733402010010922160964226777859726209933750414910570476446355945628254395996243337236132274553807309864107120535188536385621021568036360623970258619197014563522102403685917506681283}{910771774694620615581765423939161134051955660429303357925632992346112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by 672000A.

$$x=\frac{7923847882002845181309439774188096657933984031059104771715715846022994889539694246601419107202130081496635193706518322056570891905319447467793401044266301017219312648055088717366862337231995751231313859223360300343383702500954469}{87434090370683579095849480698159468868987743401213122360860767265226752000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000A}$$

Variable x cannot be equal to 0.

$$x=\frac{7923847882002845181309439774188096657933984031059104771715715846022994889539694246601419107202130081496635193706518322056570891905319447467793401044266301017219312648055088717366862337231995751231313859223360300343383702500954469}{87434090370683579095849480698159468868987743401213122360860767265226752000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000A}\text{, }x\neq 0$$