x^3+3xy-8xy=0

Solution for x^3+3xy-8xy=0 equation:

Simplifying
x3 + 3xy + -8xy = 0

Reorder the terms:
3xy + -8xy + x3 = 0

Combine like terms: 3xy + -8xy = -5xy
-5xy + x3 = 0

Solving
-5xy + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5y + x2) = 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 '(-5y + x2)' equal to zero and attempt to solve:

Simplifying
-5y + x2 = 0

Reorder the terms:
x2 + -5y = 0

Solving
x2 + -5y = 0

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

Add '5y' to each side of the equation.
x2 + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
x2 + 0 = 0 + 5y
x2 = 0 + 5y
Remove the zero:
x2 = 5y

Simplifying
x2 = 5y

The solution to this equation could not be determined.

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