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Simplifying 10x2y + -36xy2 + 32y3 = 0 Reorder the terms: -36xy2 + 10x2y + 32y3 = 0 Solving -36xy2 + 10x2y + 32y3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(-18xy + 5x2 + 16y2) = 0 Factor a trinomial. 2y((x + -2y)(5x + -8y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySubproblem 3
Set the factor '(5x + -8y)' equal to zero and attempt to solve: Simplifying 5x + -8y = 0 Solving 5x + -8y = 0 Move all terms containing x to the left, all other terms to the right. Add '8y' to each side of the equation. 5x + -8y + 8y = 0 + 8y Combine like terms: -8y + 8y = 0 5x + 0 = 0 + 8y 5x = 0 + 8y Remove the zero: 5x = 8y Divide each side by '5'. x = 1.6y Simplifying x = 1.6ySolution
x = {2y, 1.6y}
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