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

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


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

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

Reorder the terms:
((-6xy + -18x2) + -3y * (6x + 2y)) = 0
((-6xy + -18x2) + -3y * (6x + 2y)) = 0
(-6xy + -18x2 + (6x * -3y + 2y * -3y)) = 0
(-6xy + -18x2 + (-18xy + -6y2)) = 0

Reorder the terms:
(-6xy + -18xy + -18x2 + -6y2) = 0

Combine like terms: -6xy + -18xy = -24xy
(-24xy + -18x2 + -6y2) = 0

Solving
-24xy + -18x2 + -6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-6'.
-6(4xy + 3x2 + y2) = 0

Factor a trinomial.
-6((3x + y)(x + y)) = 0

Ignore the factor -6.

Subproblem 1
Set the factor '(3x + y)' equal to zero and attempt to solve:

Simplifying
3x + y = 0

Solving
3x + y = 0

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

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y

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 = {-0.3333333333y, -1y}

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