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Simplifying 32x5y2 + -162xy2 = 0 Reorder the terms: -162xy2 + 32x5y2 = 0 Solving -162xy2 + 32x5y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2xy2'. 2xy2(-81 + 16x4) = 0 Factor a difference between two squares. 2xy2((9 + 4x2)(-9 + 4x2)) = 0 Factor a difference between two squares. 2xy2((9 + 4x2)((3 + 2x)(-3 + 2x))) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'xy2' equal to zero and attempt to solve: Simplifying xy2 = 0 Solving xy2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy2 = 0 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 '(9 + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 4x2 = 0 Solving 9 + 4x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4x2 = 0 + -9 4x2 = 0 + -9 Combine like terms: 0 + -9 = -9 4x2 = -9 Divide each side by '4'. x2 = -2.25 Simplifying x2 = -2.25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 4
Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Solution
x = {-1.5, 1.5}
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