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Simplifying x3 + 8x2y + -20y2x = 0 Reorder the terms: -20xy2 + 8x2y + x3 = 0 Solving -20xy2 + 8x2y + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-20y2 + 8xy + x2) = 0 Factor a trinomial. x((-10y + -1x)(2y + -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 '(-10y + -1x)' equal to zero and attempt to solve: Simplifying -10y + -1x = 0 Reorder the terms: -1x + -10y = 0 Solving -1x + -10y = 0 Move all terms containing x to the left, all other terms to the right. Add '10y' to each side of the equation. -1x + -10y + 10y = 0 + 10y Combine like terms: -10y + 10y = 0 -1x + 0 = 0 + 10y -1x = 0 + 10y Remove the zero: -1x = 10y Divide each side by '-1'. x = -10y Simplifying x = -10ySubproblem 3
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 = 2ySolution
x = {0, -10y, 2y}
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