Solve z-2i/2-3iz=-5i

$$\frac { z - 2 i } { 2 - 3 i z } = - 5 i$$

Solve for z

$$z=-\frac{1}{2}i=-0.5i$$

Steps for Solving Linear Equation

Variable z cannot be equal to -\frac{2}{3}i since division by zero is not defined. Multiply both sides of the equation by -3iz+2.

$$z-2i=-5i\left(-3iz+2\right)$$

Use the distributive property to multiply -5i by -3iz+2.

$$z-2i=-15z-10i$$

Add 15z to both sides.

$$z-2i+15z=-10i$$

Combine z and 15z to get 16z.

$$16z-2i=-10i$$

Add 2i to both sides.

$$16z=-10i+2i$$

Add -10i and 2i to get -8i.

$$16z=-8i$$

Divide both sides by 16.

$$z=\frac{-8i}{16}$$

Divide -8i by 16 to get -\frac{1}{2}i.

$$z=-\frac{1}{2}i$$