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Simplifying 5x2 + 20xy + -60y2 = 0 Reorder the terms: 20xy + 5x2 + -60y2 = 0 Solving 20xy + 5x2 + -60y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(4xy + x2 + -12y2) = 0 Factor a trinomial. 5((x + -2y)(x + 6y)) = 0 Ignore the factor 5.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 + 6y)' equal to zero and attempt to solve: Simplifying x + 6y = 0 Solving x + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. x + 6y + -6y = 0 + -6y Combine like terms: 6y + -6y = 0 x + 0 = 0 + -6y x = 0 + -6y Remove the zero: x = -6y Simplifying x = -6ySolution
x = {2y, -6y}
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