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Simplifying 6x2 + -4xy + 12xy + -8y2 = 0 Reorder the terms: -4xy + 12xy + 6x2 + -8y2 = 0 Combine like terms: -4xy + 12xy = 8xy 8xy + 6x2 + -8y2 = 0 Solving 8xy + 6x2 + -8y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4xy + 3x2 + -4y2) = 0 Factor a trinomial. 2((3x + -2y)(x + 2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve: Simplifying 3x + -2y = 0 Solving 3x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 3x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 3x + 0 = 0 + 2y 3x = 0 + 2y Remove the zero: 3x = 2y Divide each side by '3'. x = 0.6666666667y Simplifying x = 0.6666666667ySubproblem 2
Set the factor '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 x + 0 = 0 + -2y x = 0 + -2y Remove the zero: x = -2y Simplifying x = -2ySolution
x = {0.6666666667y, -2y}
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