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Simplifying (3x + -6y)(2x + 2y) = 0 Multiply (3x + -6y) * (2x + 2y) (3x * (2x + 2y) + -6y * (2x + 2y)) = 0 ((2x * 3x + 2y * 3x) + -6y * (2x + 2y)) = 0 Reorder the terms: ((6xy + 6x2) + -6y * (2x + 2y)) = 0 ((6xy + 6x2) + -6y * (2x + 2y)) = 0 (6xy + 6x2 + (2x * -6y + 2y * -6y)) = 0 (6xy + 6x2 + (-12xy + -12y2)) = 0 Reorder the terms: (6xy + -12xy + 6x2 + -12y2) = 0 Combine like terms: 6xy + -12xy = -6xy (-6xy + 6x2 + -12y2) = 0 Solving -6xy + 6x2 + -12y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-1xy + x2 + -2y2) = 0 Factor a trinomial. 6((x + -2y)(x + y)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySubproblem 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 = {2y, -1y}
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