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Simplifying x3 + -14x2y + 24xy2 = 0 Reorder the terms: 24xy2 + -14x2y + x3 = 0 Solving 24xy2 + -14x2y + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(24y2 + -14xy + x2) = 0 Factor a trinomial. x((2y + -1x)(12y + -1x)) = 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 '(2y + -1x)' equal to zero and attempt to solve: Simplifying 2y + -1x = 0 Reorder the terms: -1x + 2y = 0 Solving -1x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. -1x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 -1x + 0 = 0 + -2y -1x = 0 + -2y Remove the zero: -1x = -2y Divide each side by '-1'. x = 2y Simplifying x = 2ySubproblem 3
Set the factor '(12y + -1x)' equal to zero and attempt to solve: Simplifying 12y + -1x = 0 Reorder the terms: -1x + 12y = 0 Solving -1x + 12y = 0 Move all terms containing x to the left, all other terms to the right. Add '-12y' to each side of the equation. -1x + 12y + -12y = 0 + -12y Combine like terms: 12y + -12y = 0 -1x + 0 = 0 + -12y -1x = 0 + -12y Remove the zero: -1x = -12y Divide each side by '-1'. x = 12y Simplifying x = 12ySolution
x = {0, 2y, 12y}
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