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Simplifying -4x2(x4 + -81) = 0 Reorder the terms: -4x2(-81 + x4) = 0 (-81 * -4x2 + x4 * -4x2) = 0 (324x2 + -4x6) = 0 Solving 324x2 + -4x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(81 + -1x4) = 0 Factor a difference between two squares. 4x2((9 + x2)(9 + -1x2)) = 0 Factor a difference between two squares. 4x2((9 + x2)((3 + x)(3 + -1x))) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(9 + x2)' equal to zero and attempt to solve: Simplifying 9 + x2 = 0 Solving 9 + x2 = 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 + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x2 = 0 + -9 x2 = 0 + -9 Combine like terms: 0 + -9 = -9 x2 = -9 Simplifying x2 = -9 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 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 4
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, -3, 3}
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