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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 = -1ySubproblem 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 = -1ySolution
x = {-1y, -1y}
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