Solve x-12/8+x-12/13*3+x+1*2=0

$$\frac{ x-12 }{ 8 } + \frac{ x-12 }{ 13 \cdot 3 } +x+1 \cdot 2 = 0$$

Solve for x

$$x=-\frac{60}{359}\approx -0.167130919$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8.

$$x-12+\frac{8}{39}\left(x-12\right)+8x+8\times 2=0$$

Use the distributive property to multiply \frac{8}{39} by x-12.

$$x-12+\frac{8}{39}x+\frac{8}{39}\left(-12\right)+8x+8\times 2=0$$

Express \frac{8}{39}\left(-12\right) as a single fraction.

$$x-12+\frac{8}{39}x+\frac{8\left(-12\right)}{39}+8x+8\times 2=0$$

Multiply 8 and -12 to get -96.

$$x-12+\frac{8}{39}x+\frac{-96}{39}+8x+8\times 2=0$$

Reduce the fraction \frac{-96}{39} to lowest terms by extracting and canceling out 3.

$$x-12+\frac{8}{39}x-\frac{32}{13}+8x+8\times 2=0$$

Combine x and \frac{8}{39}x to get \frac{47}{39}x.

$$\frac{47}{39}x-12-\frac{32}{13}+8x+8\times 2=0$$

Convert -12 to fraction -\frac{156}{13}.

$$\frac{47}{39}x-\frac{156}{13}-\frac{32}{13}+8x+8\times 2=0$$

Since -\frac{156}{13} and \frac{32}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{47}{39}x+\frac{-156-32}{13}+8x+8\times 2=0$$

Subtract 32 from -156 to get -188.

$$\frac{47}{39}x-\frac{188}{13}+8x+8\times 2=0$$

Combine \frac{47}{39}x and 8x to get \frac{359}{39}x.

$$\frac{359}{39}x-\frac{188}{13}+8\times 2=0$$

Multiply 8 and 2 to get 16.

$$\frac{359}{39}x-\frac{188}{13}+16=0$$

Convert 16 to fraction \frac{208}{13}.

$$\frac{359}{39}x-\frac{188}{13}+\frac{208}{13}=0$$

Since -\frac{188}{13} and \frac{208}{13} have the same denominator, add them by adding their numerators.

$$\frac{359}{39}x+\frac{-188+208}{13}=0$$

Add -188 and 208 to get 20.

$$\frac{359}{39}x+\frac{20}{13}=0$$

Subtract \frac{20}{13} from both sides. Anything subtracted from zero gives its negation.

$$\frac{359}{39}x=-\frac{20}{13}$$

Multiply both sides by \frac{39}{359}, the reciprocal of \frac{359}{39}.

$$x=-\frac{20}{13}\times \frac{39}{359}$$

Multiply -\frac{20}{13} times \frac{39}{359} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-20\times 39}{13\times 359}$$

Do the multiplications in the fraction \frac{-20\times 39}{13\times 359}.

$$x=\frac{-780}{4667}$$

Reduce the fraction \frac{-780}{4667} to lowest terms by extracting and canceling out 13.

$$x=-\frac{60}{359}$$