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Simplifying 9x3 + -6x2y + xy2 = 0 Reorder the terms: xy2 + -6x2y + 9x3 = 0 Solving xy2 + -6x2y + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(y2 + -6xy + 9x2) = 0 Factor a trinomial. x((y + -3x)(y + -3x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(y + -3x)' equal to zero and attempt to solve: Simplifying y + -3x = 0 Reorder the terms: -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 = 0.3333333333ySubproblem 3
Set the factor '(y + -3x)' equal to zero and attempt to solve: Simplifying y + -3x = 0 Reorder the terms: -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 = {0, 0.3333333333y, 0.3333333333y}
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