(2x-2y)(3x-3y)=0

Solution for (2x-2y)(3x-3y)=0 equation:

Simplifying
(2x + -2y)(3x + -3y) = 0

Multiply (2x + -2y) * (3x + -3y)
(2x * (3x + -3y) + -2y * (3x + -3y)) = 0
((3x * 2x + -3y * 2x) + -2y * (3x + -3y)) = 0

Reorder the terms:
((-6xy + 6x2) + -2y * (3x + -3y)) = 0
((-6xy + 6x2) + -2y * (3x + -3y)) = 0
(-6xy + 6x2 + (3x * -2y + -3y * -2y)) = 0
(-6xy + 6x2 + (-6xy + 6y2)) = 0

Reorder the terms:
(-6xy + -6xy + 6x2 + 6y2) = 0

Combine like terms: -6xy + -6xy = -12xy
(-12xy + 6x2 + 6y2) = 0

Solving
-12xy + 6x2 + 6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2xy + x2 + y2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

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