(-4x-4y)(5x+5y)=0

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Solution for (-4x-4y)(5x+5y)=0 equation:


Simplifying
(-4x + -4y)(5x + 5y) = 0

Multiply (-4x + -4y) * (5x + 5y)
(-4x * (5x + 5y) + -4y * (5x + 5y)) = 0
((5x * -4x + 5y * -4x) + -4y * (5x + 5y)) = 0

Reorder the terms:
((-20xy + -20x2) + -4y * (5x + 5y)) = 0
((-20xy + -20x2) + -4y * (5x + 5y)) = 0
(-20xy + -20x2 + (5x * -4y + 5y * -4y)) = 0
(-20xy + -20x2 + (-20xy + -20y2)) = 0

Reorder the terms:
(-20xy + -20xy + -20x2 + -20y2) = 0

Combine like terms: -20xy + -20xy = -40xy
(-40xy + -20x2 + -20y2) = 0

Solving
-40xy + -20x2 + -20y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-20'.
-20(2xy + x2 + y2) = 0

Factor a trinomial.
-20((x + y)(x + y)) = 0

Ignore the factor -20.

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 + 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 = {-1y, -1y}

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