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Simplifying -8x2 + 28xy + 60y2 = 0 Reorder the terms: 28xy + -8x2 + 60y2 = 0 Solving 28xy + -8x2 + 60y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(7xy + -2x2 + 15y2) = 0 Factor a trinomial. 4((-2x + -3y)(x + -5y)) = 0 Ignore the factor 4.Subproblem 1
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 = -1.5ySubproblem 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 = {-1.5y, 5y}
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