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Simplifying 2x3 + -40x + 192xy2 = 0 Reorder the terms: -40x + 192xy2 + 2x3 = 0 Solving -40x + 192xy2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-20 + 96y2 + x2) = 0 Factor a trinomial. 2x((8y + -1x)(12y + -1x)) = 0 Ignore the factor 2.Subproblem 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 '(8y + -1x)' equal to zero and attempt to solve: Simplifying 8y + -1x = 0 Reorder the terms: -1x + 8y = 0 Solving -1x + 8y = 0 Move all terms containing x to the left, all other terms to the right. Add '-8y' to each side of the equation. -1x + 8y + -8y = 0 + -8y Combine like terms: 8y + -8y = 0 -1x + 0 = 0 + -8y -1x = 0 + -8y Remove the zero: -1x = -8y Divide each side by '-1'. x = 8y Simplifying x = 8ySubproblem 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, 8y, 12y}
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