x^3-2yx^2=0

Solution for x^3-2yx^2=0 equation:

Simplifying
x3 + -2yx2 = 0

Reorder the terms:
-2x2y + x3 = 0

Solving
-2x2y + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-2y + x) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

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

Simplifying
-2y + x = 0

Reorder the terms:
x + -2y = 0

Solving
x + -2y = 0

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

Add '2y' to each side of the equation.
x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
x + 0 = 0 + 2y
x = 0 + 2y
Remove the zero:
x = 2y

Simplifying
x = 2y
Solution
x = {0, 2y}