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Simplifying x5 + -15x3 + -16x = 0 Reorder the terms: -16x + -15x3 + x5 = 0 Solving -16x + -15x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-16 + -15x2 + x4) = 0 Factor a trinomial. x((-1 + -1x2)(16 + -1x2)) = 0 Factor a difference between two squares. x((-1 + -1x2)((4 + x)(4 + -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 '(-1 + -1x2)' equal to zero and attempt to solve: Simplifying -1 + -1x2 = 0 Solving -1 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x2 = 0 + 1 -1x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1x2 = 1 Divide each side by '-1'. x2 = -1 Simplifying x2 = -1 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 4
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0, -4, 4}
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