Solve 5+4i-40/2-4a/4-4a-(-20)/8=0

$$5 + \frac { 4 i - 40 } { 2 } - \frac { 4 a } { 4 } - \frac { 4 a - ( - 20 ) } { 8 } = 0$$

Solve for a

$$a=-\frac{35}{3}+\frac{4}{3}i\approx -11.666666667+1.333333333i$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 2,4,8.

$$40+4\left(4i-40\right)-2\times 4a-\left(4a-\left(-20\right)\right)=0$$

Use the distributive property to multiply 4 by 4i-40.

$$40+16i-160-2\times 4a-\left(4a-\left(-20\right)\right)=0$$

Combine the real and imaginary parts in 40+16i-160.

$$-2\times 4a-\left(4a-\left(-20\right)\right)+40-160+16i=0$$

Add 40 to -160.

$$-2\times 4a-\left(4a-\left(-20\right)\right)-120+16i=0$$

Multiply -2 and 4 to get -8.

$$-8a-\left(4a-\left(-20\right)\right)-120+16i=0$$

The opposite of -20 is 20.

$$-8a-\left(4a+20\right)-120+16i=0$$

To find the opposite of 4a+20, find the opposite of each term.

$$-8a-4a-20-120+16i=0$$

Add -20 to -120.

$$-8a-4a-140+16i=0$$

Combine -8a and -4a to get -12a.

$$-12a-140+16i=0$$

Add 140 to both sides. Anything plus zero gives itself.

$$-12a+16i=140$$

Subtract 16i from both sides.

$$-12a=140-16i$$

Divide both sides by -12.

$$a=\frac{140-16i}{-12}$$

Divide 140-16i by -12 to get -\frac{35}{3}+\frac{4}{3}i.

$$a=-\frac{35}{3}+\frac{4}{3}i$$