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

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

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

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

Reorder the terms:
((-9xy + 9x2) + -3y * (3x + -3y)) = 0
((-9xy + 9x2) + -3y * (3x + -3y)) = 0
(-9xy + 9x2 + (3x * -3y + -3y * -3y)) = 0
(-9xy + 9x2 + (-9xy + 9y2)) = 0

Reorder the terms:
(-9xy + -9xy + 9x2 + 9y2) = 0

Combine like terms: -9xy + -9xy = -18xy
(-18xy + 9x2 + 9y2) = 0

Solving
-18xy + 9x2 + 9y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-2xy + x2 + y2) = 0

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

Ignore the factor 9.
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}