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

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

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

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

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

Reorder the terms:
(6xy + -2xy + 2x2 + -6y2) = 0

Combine like terms: 6xy + -2xy = 4xy
(4xy + 2x2 + -6y2) = 0

Solving
4xy + 2x2 + -6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2xy + x2 + -3y2) = 0

Factor a trinomial.
2((x + -1y)(x + 3y)) = 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 + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

Add '-3y' to each side of the equation.
x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
x + 0 = 0 + -3y
x = 0 + -3y
Remove the zero:
x = -3y

Simplifying
x = -3y
Solution
x = {y, -3y}