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Simplifying 8x3 + -2x2y + -15xy2 = 0 Reorder the terms: -15xy2 + -2x2y + 8x3 = 0 Solving -15xy2 + -2x2y + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-15y2 + -2xy + 8x2) = 0 Factor a trinomial. x((-5y + -4x)(3y + -2x)) = 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 '(-5y + -4x)' equal to zero and attempt to solve: Simplifying -5y + -4x = 0 Reorder the terms: -4x + -5y = 0 Solving -4x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. -4x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 -4x + 0 = 0 + 5y -4x = 0 + 5y Remove the zero: -4x = 5y Divide each side by '-4'. x = -1.25y Simplifying x = -1.25ySubproblem 3
Set the factor '(3y + -2x)' equal to zero and attempt to solve: Simplifying 3y + -2x = 0 Reorder the terms: -2x + 3y = 0 Solving -2x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. -2x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 -2x + 0 = 0 + -3y -2x = 0 + -3y Remove the zero: -2x = -3y Divide each side by '-2'. x = 1.5y Simplifying x = 1.5ySolution
x = {0, -1.25y, 1.5y}
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