(-5x-2y)(2x+2y)=0

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Solution for (-5x-2y)(2x+2y)=0 equation: 


Simplifying
(-5x + -2y)(2x + 2y) = 0

Multiply (-5x + -2y) * (2x + 2y)
(-5x * (2x + 2y) + -2y * (2x + 2y)) = 0
((2x * -5x + 2y * -5x) + -2y * (2x + 2y)) = 0

Reorder the terms:
((-10xy + -10x2) + -2y * (2x + 2y)) = 0
((-10xy + -10x2) + -2y * (2x + 2y)) = 0
(-10xy + -10x2 + (2x * -2y + 2y * -2y)) = 0
(-10xy + -10x2 + (-4xy + -4y2)) = 0

Reorder the terms:
(-10xy + -4xy + -10x2 + -4y2) = 0

Combine like terms: -10xy + -4xy = -14xy
(-14xy + -10x2 + -4y2) = 0

Solving
-14xy + -10x2 + -4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(7xy + 5x2 + 2y2) = 0

Factor a trinomial.
-2((5x + 2y)(x + y)) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(5x + 2y)' equal to zero and attempt to solve:

Simplifying
5x + 2y = 0

Solving
5x + 2y = 0

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

Add '-2y' to each side of the equation.
5x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
5x + 0 = 0 + -2y
5x = 0 + -2y
Remove the zero:
5x = -2y

Divide each side by '5'.
x = -0.4y

Simplifying
x = -0.4y

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 = {-0.4y, -1y}

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