Solve 100(1/5+1/5i+1/-5i)=100/5+5i+frac{60+80i}{5-5i}-X

$$100 ( \frac { 1 } { 5 } + \frac { 1 } { 5 i } + \frac { 1 } { - 5 i } ) = \frac { 100 } { 5 + 5 i } + \frac { 60 + 80 i } { 5 - 5 i } - X$$

Solve for X

$$X=-12+4i$$

Steps for Solving Linear Equation

Multiply both numerator and denominator of \frac{1}{5i} by imaginary unit i.

$$100\left(\frac{1}{5}+\frac{i}{-5}+\frac{1}{-5i}\right)=\frac{100}{5+5i}+\frac{60+80i}{5-5i}-X$$

Divide i by -5 to get -\frac{1}{5}i.

$$100\left(\frac{1}{5}-\frac{1}{5}i+\frac{1}{-5i}\right)=\frac{100}{5+5i}+\frac{60+80i}{5-5i}-X$$

Multiply both numerator and denominator of \frac{1}{-5i} by imaginary unit i.

$$100\left(\frac{1}{5}-\frac{1}{5}i+\frac{i}{5}\right)=\frac{100}{5+5i}+\frac{60+80i}{5-5i}-X$$

Divide i by 5 to get \frac{1}{5}i.

$$100\left(\frac{1}{5}-\frac{1}{5}i+\frac{1}{5}i\right)=\frac{100}{5+5i}+\frac{60+80i}{5-5i}-X$$

Do the additions in \frac{1}{5}-\frac{1}{5}i+\frac{1}{5}i.

$$100\times \frac{1}{5}=\frac{100}{5+5i}+\frac{60+80i}{5-5i}-X$$

Multiply 100 and \frac{1}{5} to get 20.

$$20=\frac{100}{5+5i}+\frac{60+80i}{5-5i}-X$$

Multiply both numerator and denominator of \frac{100}{5+5i} by the complex conjugate of the denominator, 5-5i.

$$20=\frac{100\left(5-5i\right)}{\left(5+5i\right)\left(5-5i\right)}+\frac{60+80i}{5-5i}-X$$

Do the multiplications in \frac{100\left(5-5i\right)}{\left(5+5i\right)\left(5-5i\right)}.

$$20=\frac{500-500i}{50}+\frac{60+80i}{5-5i}-X$$

Divide 500-500i by 50 to get 10-10i.

$$20=10-10i+\frac{60+80i}{5-5i}-X$$

Multiply both numerator and denominator of \frac{60+80i}{5-5i} by the complex conjugate of the denominator, 5+5i.

$$20=10-10i+\frac{\left(60+80i\right)\left(5+5i\right)}{\left(5-5i\right)\left(5+5i\right)}-X$$

Do the multiplications in \frac{\left(60+80i\right)\left(5+5i\right)}{\left(5-5i\right)\left(5+5i\right)}.

$$20=10-10i+\frac{-100+700i}{50}-X$$

Divide -100+700i by 50 to get -2+14i.

$$20=10-10i+\left(-2+14i\right)-X$$

Do the additions in 10-10i+\left(-2+14i\right).

$$20=-X+8+4i$$

Swap sides so that all variable terms are on the left hand side.

$$-X+8+4i=20$$

Subtract 8 from both sides.

$$-X+4i=20-8$$

Subtract 8 from 20 to get 12.

$$-X+4i=12$$

Subtract 4i from both sides.

$$-X=12-4i$$

Divide both sides by -1.

$$X=\frac{12-4i}{-1}$$

Divide 12-4i by -1 to get -12+4i.

$$X=-12+4i$$