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Simplifying 5x3 + 10x2y + -75xy2 = 0 Reorder the terms: -75xy2 + 10x2y + 5x3 = 0 Solving -75xy2 + 10x2y + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(-15y2 + 2xy + x2) = 0 Factor a trinomial. 5x((-5y + -1x)(3y + -1x)) = 0 Ignore the factor 5.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 '(3y + -1x)' equal to zero and attempt to solve: Simplifying 3y + -1x = 0 Reorder the terms: -1x + 3y = 0 Solving -1x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. -1x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 -1x + 0 = 0 + -3y -1x = 0 + -3y Remove the zero: -1x = -3y Divide each side by '-1'. x = 3y Simplifying x = 3ySolution
x = {0, -5y, 3y}
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