(3x-6y)(2x+2y)=

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Solution for (3x-6y)(2x+2y)= equation: 


Simplifying
(3x + -6y)(2x + 2y) = 0

Multiply (3x + -6y) * (2x + 2y)
(3x * (2x + 2y) + -6y * (2x + 2y)) = 0
((2x * 3x + 2y * 3x) + -6y * (2x + 2y)) = 0

Reorder the terms:
((6xy + 6x2) + -6y * (2x + 2y)) = 0
((6xy + 6x2) + -6y * (2x + 2y)) = 0
(6xy + 6x2 + (2x * -6y + 2y * -6y)) = 0
(6xy + 6x2 + (-12xy + -12y2)) = 0

Reorder the terms:
(6xy + -12xy + 6x2 + -12y2) = 0

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

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

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1xy + x2 + -2y2) = 0

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

Ignore the factor 6.

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 + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {2y, -1y}

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