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Simplifying 4x2 + 8xy + -60y2 = 0 Reorder the terms: 8xy + 4x2 + -60y2 = 0 Solving 8xy + 4x2 + -60y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2xy + x2 + -15y2) = 0 Factor a trinomial. 4((x + -3y)(x + 5y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(x + -3y)' equal to zero and attempt to solve: Simplifying x + -3y = 0 Solving x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 x + 0 = 0 + 3y x = 0 + 3y Remove the zero: x = 3y Simplifying x = 3ySubproblem 2
Set the factor '(x + 5y)' equal to zero and attempt to solve: Simplifying x + 5y = 0 Solving x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 x + 0 = 0 + -5y x = 0 + -5y Remove the zero: x = -5y Simplifying x = -5ySolution
x = {3y, -5y}
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