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Simplifying 5x3 + 35x2y + 60xy2 = 0 Reorder the terms: 60xy2 + 35x2y + 5x3 = 0 Solving 60xy2 + 35x2y + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(12y2 + 7xy + x2) = 0 Factor a trinomial. 5x((4y + x)(3y + x)) = 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 '(4y + x)' equal to zero and attempt to solve: Simplifying 4y + x = 0 Reorder the terms: x + 4y = 0 Solving x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 x + 0 = 0 + -4y x = 0 + -4y Remove the zero: x = -4y Simplifying x = -4ySubproblem 3
Set the factor '(3y + x)' equal to zero and attempt to solve: Simplifying 3y + x = 0 Reorder the terms: x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3ySolution
x = {0, -4y, -3y}
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