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Simplifying 2x(x2 + 3)(x2 + -81) = 0 Reorder the terms: 2x(3 + x2)(x2 + -81) = 0 Reorder the terms: 2x(3 + x2)(-81 + x2) = 0 Multiply (3 + x2) * (-81 + x2) 2x(3(-81 + x2) + x2(-81 + x2)) = 0 2x((-81 * 3 + x2 * 3) + x2(-81 + x2)) = 0 2x((-243 + 3x2) + x2(-81 + x2)) = 0 2x(-243 + 3x2 + (-81 * x2 + x2 * x2)) = 0 2x(-243 + 3x2 + (-81x2 + x4)) = 0 Combine like terms: 3x2 + -81x2 = -78x2 2x(-243 + -78x2 + x4) = 0 (-243 * 2x + -78x2 * 2x + x4 * 2x) = 0 (-486x + -156x3 + 2x5) = 0 Solving -486x + -156x3 + 2x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-243 + -78x2 + x4) = 0 Factor a trinomial. 2x((-3 + -1x2)(81 + -1x2)) = 0 Factor a difference between two squares. 2x((-3 + -1x2)((9 + x)(9 + -1x))) = 0 Ignore the factor 2.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 '(-3 + -1x2)' equal to zero and attempt to solve: Simplifying -3 + -1x2 = 0 Solving -3 + -1x2 = 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 + -1x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x2 = 0 + 3 -1x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x2 = 3 Divide each side by '-1'. x2 = -3 Simplifying x2 = -3 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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 4
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {0, -9, 9}
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