(-8x-8y)(2x+8y)=0

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Solution for (-8x-8y)(2x+8y)=0 equation: 


Simplifying
(-8x + -8y)(2x + 8y) = 0

Multiply (-8x + -8y) * (2x + 8y)
(-8x * (2x + 8y) + -8y * (2x + 8y)) = 0
((2x * -8x + 8y * -8x) + -8y * (2x + 8y)) = 0

Reorder the terms:
((-64xy + -16x2) + -8y * (2x + 8y)) = 0
((-64xy + -16x2) + -8y * (2x + 8y)) = 0
(-64xy + -16x2 + (2x * -8y + 8y * -8y)) = 0
(-64xy + -16x2 + (-16xy + -64y2)) = 0

Reorder the terms:
(-64xy + -16xy + -16x2 + -64y2) = 0

Combine like terms: -64xy + -16xy = -80xy
(-80xy + -16x2 + -64y2) = 0

Solving
-80xy + -16x2 + -64y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-16'.
-16(5xy + x2 + 4y2) = 0

Factor a trinomial.
-16((x + y)(x + 4y)) = 0

Ignore the factor -16.

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 + 4y)' equal to zero and attempt to solve:

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

Add '-4y' to each side of the equation.
x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
x + 0 = 0 + -4y
x = 0 + -4y
Remove the zero:
x = -4y

Simplifying
x = -4y
Solution
x = {-1y, -4y}

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