Solve -3z=216a-36(37-16ia/-20)

$$- 3 z = 216 a - 36 ( \frac { 37 - 16 i a } { - 20 } )$$

Solve for a

$$a=\left(-\frac{25}{1832}-\frac{5}{2748}i\right)z+\left(-\frac{555}{1832}-\frac{37}{916}i\right)$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -20.

$$60z=-4320a-36\left(37-16ia\right)$$

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

$$-4320a-36\left(37-16ia\right)=60z$$

Use the distributive property to multiply -36 by 37-16ia.

$$-4320a-1332+576ia=60z$$

Combine -4320a and 576ia to get \left(-4320+576i\right)a.

$$\left(-4320+576i\right)a-1332=60z$$

Add 1332 to both sides.

$$\left(-4320+576i\right)a=60z+1332$$

Divide both sides by -4320+576i.

$$\frac{\left(-4320+576i\right)a}{-4320+576i}=\frac{60z+1332}{-4320+576i}$$

Dividing by -4320+576i undoes the multiplication by -4320+576i.

$$a=\frac{60z+1332}{-4320+576i}$$

Divide 60z+1332 by -4320+576i.

$$a=\left(-\frac{25}{1832}-\frac{5}{2748}i\right)z+\left(-\frac{555}{1832}-\frac{37}{916}i\right)$$

Solve for z

$$z=\left(-72+\frac{48}{5}i\right)a-\frac{111}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -20.

$$60z=-4320a-36\left(37-16ia\right)$$

Use the distributive property to multiply -36 by 37-16ia.

$$60z=-4320a-1332+576ia$$

Combine -4320a and 576ia to get \left(-4320+576i\right)a.

$$60z=\left(-4320+576i\right)a-1332$$

Divide both sides by 60.

$$\frac{60z}{60}=\frac{\left(-4320+576i\right)a-1332}{60}$$

Dividing by 60 undoes the multiplication by 60.

$$z=\frac{\left(-4320+576i\right)a-1332}{60}$$

Divide \left(-4320+576i\right)a-1332 by 60.

$$z=\left(-72+\frac{48}{5}i\right)a-\frac{111}{5}$$