6x^3y^3-12x^2y^3+6xy^3=0

Solution for 6x^3y^3-12x^2y^3+6xy^3=0 equation:

Simplifying
6x3y3 + -12x2y3 + 6xy3 = 0

Reorder the terms:
6xy3 + -12x2y3 + 6x3y3 = 0

Solving
6xy3 + -12x2y3 + 6x3y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6xy3'.
6xy3(1 + -2x + x2) = 0

Factor a trinomial.
6xy3((1 + -1x)(1 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'xy3' equal to zero and attempt to solve:

Simplifying
xy3 = 0

Solving
xy3 = 0

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

Simplifying
xy3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {1, 1}