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Simplifying 32x2 + 8xy + -60y2 = 0 Reorder the terms: 8xy + 32x2 + -60y2 = 0 Solving 8xy + 32x2 + -60y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2xy + 8x2 + -15y2) = 0 Factor a trinomial. 4((4x + -5y)(2x + 3y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4x + -5y)' equal to zero and attempt to solve: Simplifying 4x + -5y = 0 Solving 4x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 4x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 4x + 0 = 0 + 5y 4x = 0 + 5y Remove the zero: 4x = 5y Divide each side by '4'. x = 1.25y Simplifying x = 1.25ySubproblem 2
Set the factor '(2x + 3y)' equal to zero and attempt to solve: Simplifying 2x + 3y = 0 Solving 2x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 2x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 2x + 0 = 0 + -3y 2x = 0 + -3y Remove the zero: 2x = -3y Divide each side by '2'. x = -1.5y Simplifying x = -1.5ySolution
x = {1.25y, -1.5y}
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