(2x-4y)(2x-4y)=0

Solution for (2x-4y)(2x-4y)=0 equation:

Simplifying
(2x + -4y)(2x + -4y) = 0

Multiply (2x + -4y) * (2x + -4y)
(2x * (2x + -4y) + -4y * (2x + -4y)) = 0
((2x * 2x + -4y * 2x) + -4y * (2x + -4y)) = 0

Reorder the terms:
((-8xy + 4x2) + -4y * (2x + -4y)) = 0
((-8xy + 4x2) + -4y * (2x + -4y)) = 0
(-8xy + 4x2 + (2x * -4y + -4y * -4y)) = 0
(-8xy + 4x2 + (-8xy + 16y2)) = 0

Reorder the terms:
(-8xy + -8xy + 4x2 + 16y2) = 0

Combine like terms: -8xy + -8xy = -16xy
(-16xy + 4x2 + 16y2) = 0

Solving
-16xy + 4x2 + 16y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4xy + x2 + 4y2) = 0

Factor a trinomial.
4((x + -2y)(x + -2y)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(x + -2y)' equal to zero and attempt to solve:

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

Add '2y' to each side of the equation.
x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
x + 0 = 0 + 2y
x = 0 + 2y
Remove the zero:
x = 2y

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

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

Add '2y' to each side of the equation.
x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
x + 0 = 0 + 2y
x = 0 + 2y
Remove the zero:
x = 2y

Simplifying
x = 2y
Solution
x = {2y, 2y}