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Simplifying 54x2 + -126xy + -48y2 = 0 Reorder the terms: -126xy + 54x2 + -48y2 = 0 Solving -126xy + 54x2 + -48y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-21xy + 9x2 + -8y2) = 0 Factor a trinomial. 6((3x + -8y)(3x + y)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3x + -8y)' equal to zero and attempt to solve: Simplifying 3x + -8y = 0 Solving 3x + -8y = 0 Move all terms containing x to the left, all other terms to the right. Add '8y' to each side of the equation. 3x + -8y + 8y = 0 + 8y Combine like terms: -8y + 8y = 0 3x + 0 = 0 + 8y 3x = 0 + 8y Remove the zero: 3x = 8y Divide each side by '3'. x = 2.666666667y Simplifying x = 2.666666667ySubproblem 2
Set the factor '(3x + y)' equal to zero and attempt to solve: Simplifying 3x + y = 0 Solving 3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 3x + 0 = 0 + -1y 3x = 0 + -1y Remove the zero: 3x = -1y Divide each side by '3'. x = -0.3333333333y Simplifying x = -0.3333333333ySolution
x = {2.666666667y, -0.3333333333y}
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