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Simplifying 12x2 + -12xy + -24y2 = 0 Reorder the terms: -12xy + 12x2 + -24y2 = 0 Solving -12xy + 12x2 + -24y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-1xy + x2 + -2y2) = 0 Factor a trinomial. 12((x + -2y)(x + y)) = 0 Ignore the factor 12.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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