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Simplifying x5 + -6x3 + -27x = 0 Reorder the terms: -27x + -6x3 + x5 = 0 Solving -27x + -6x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-27 + -6x2 + x4) = 0 Factor a trinomial. x((-3 + -1x2)(9 + -1x2)) = 0 Factor a difference between two squares. x((-3 + -1x2)((3 + x)(3 + -1x))) = 0Subproblem 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 '(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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