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Simplifying 2x3 + 6x2y + -20xy2 = 0 Reorder the terms: -20xy2 + 6x2y + 2x3 = 0 Solving -20xy2 + 6x2y + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-10y2 + 3xy + x2) = 0 Factor a trinomial. 2x((-5y + -1x)(2y + -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 '(-5y + -1x)' equal to zero and attempt to solve: Simplifying -5y + -1x = 0 Reorder the terms: -1x + -5y = 0 Solving -1x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. -1x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 -1x + 0 = 0 + 5y -1x = 0 + 5y Remove the zero: -1x = 5y Divide each side by '-1'. x = -5y Simplifying x = -5ySubproblem 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, -5y, 2y}
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