2x^3-3xy=x

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

Simplifying
2x3 + -3xy = x

Reorder the terms:
-3xy + 2x3 = x

Solving
-3xy + 2x3 = x

Solving for variable 'x'.

Reorder the terms:
-1x + -3xy + 2x3 = x + -1x

Combine like terms: x + -1x = 0
-1x + -3xy + 2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + -3y + 2x2) = 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 '(-1 + -3y + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + -3y + 2x2 = 0

Reorder the terms:
-1 + 2x2 + -3y = 0

Solving
-1 + 2x2 + -3y = 0

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

Add '1' to each side of the equation.
-1 + 2x2 + 1 + -3y = 0 + 1

Reorder the terms:
-1 + 1 + 2x2 + -3y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x2 + -3y = 0 + 1
2x2 + -3y = 0 + 1

Combine like terms: 0 + 1 = 1
2x2 + -3y = 1

Add '3y' to each side of the equation.
2x2 + -3y + 3y = 1 + 3y

Combine like terms: -3y + 3y = 0
2x2 + 0 = 1 + 3y
2x2 = 1 + 3y

Divide each side by '2'.
x2 = 0.5 + 1.5y

Simplifying
x2 = 0.5 + 1.5y

The solution to this equation could not be determined.

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