2xy-x^3=0

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

Simplifying
2xy + -1x3 = 0

Solving
2xy + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2y + -1x2) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(2y + -1x2)' equal to zero and attempt to solve:

Simplifying
2y + -1x2 = 0

Reorder the terms:
-1x2 + 2y = 0

Solving
-1x2 + 2y = 0

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

Add '-2y' to each side of the equation.
-1x2 + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-1x2 + 0 = 0 + -2y
-1x2 = 0 + -2y
Remove the zero:
-1x2 = -2y

Divide each side by '-1'.
x2 = 2y

Simplifying
x2 = 2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}