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Simplifying 12x2 + -2xy + -10y2 = 0 Reorder the terms: -2xy + 12x2 + -10y2 = 0 Solving -2xy + 12x2 + -10y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1xy + 6x2 + -5y2) = 0 Factor a trinomial. 2((x + -1y)(6x + 5y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySubproblem 2
Set the factor '(6x + 5y)' equal to zero and attempt to solve: Simplifying 6x + 5y = 0 Solving 6x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 6x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 6x + 0 = 0 + -5y 6x = 0 + -5y Remove the zero: 6x = -5y Divide each side by '6'. x = -0.8333333333y Simplifying x = -0.8333333333ySolution
x = {y, -0.8333333333y}
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