z^3=2iz^2

Solution for z^3=2iz^2 equation:

Simplifying
z3 = 2iz2

Solving
z3 = 2iz2

Solving for variable 'z'.

Reorder the terms:
-2iz2 + z3 = 2iz2 + -2iz2

Combine like terms: 2iz2 + -2iz2 = 0
-2iz2 + z3 = 0

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(-2i + z) = 0

Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

Move all terms containing z to the left, all other terms to the right.

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(-2i + z)' equal to zero and attempt to solve:

Simplifying
-2i + z = 0

Solving
-2i + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '2i' to each side of the equation.
-2i + 2i + z = 0 + 2i

Combine like terms: -2i + 2i = 0
0 + z = 0 + 2i
z = 0 + 2i
Remove the zero:
z = 2i

Simplifying
z = 2i
Solution
z = {0, 2i}