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Simplifying 12x2 + -8xy + -20y2 = 0 Reorder the terms: -8xy + 12x2 + -20y2 = 0 Solving -8xy + 12x2 + -20y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2xy + 3x2 + -5y2) = 0 Factor a trinomial. 4((3x + -5y)(x + y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3x + -5y)' equal to zero and attempt to solve: Simplifying 3x + -5y = 0 Solving 3x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 3x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 3x + 0 = 0 + 5y 3x = 0 + 5y Remove the zero: 3x = 5y Divide each side by '3'. x = 1.666666667y Simplifying x = 1.666666667ySubproblem 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 = {1.666666667y, -1y}
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