(2x-2y)(x+2y)=

Solution for (2x-2y)(x+2y)= equation:

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

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

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

Reorder the terms:
(4xy + -2xy + 2x2 + -4y2) = 0

Combine like terms: 4xy + -2xy = 2xy
(2xy + 2x2 + -4y2) = 0

Solving
2xy + 2x2 + -4y2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
2((x + -1y)(x + 2y)) = 0

Ignore the factor 2.
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 + 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 = {y, -2y}