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

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


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

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

Reorder the terms:
((-18xy + -18x2) + -6y * (6x + 6y)) = 0
((-18xy + -18x2) + -6y * (6x + 6y)) = 0
(-18xy + -18x2 + (6x * -6y + 6y * -6y)) = 0
(-18xy + -18x2 + (-36xy + -36y2)) = 0

Reorder the terms:
(-18xy + -36xy + -18x2 + -36y2) = 0

Combine like terms: -18xy + -36xy = -54xy
(-54xy + -18x2 + -36y2) = 0

Solving
-54xy + -18x2 + -36y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-18'.
-18(3xy + x2 + 2y2) = 0

Factor a trinomial.
-18((x + y)(x + 2y)) = 0

Ignore the factor -18.

Subproblem 1
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

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 = {-1y, -2y}

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