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Simplifying x((x2) + -4)((x2) + 1) = 0 x(x2 + -4)((x2) + 1) = 0 Reorder the terms: x(-4 + x2)((x2) + 1) = 0 x(-4 + x2)(x2 + 1) = 0 Reorder the terms: x(-4 + x2)(1 + x2) = 0 Multiply (-4 + x2) * (1 + x2) x(-4(1 + x2) + x2(1 + x2)) = 0 x((1 * -4 + x2 * -4) + x2(1 + x2)) = 0 x((-4 + -4x2) + x2(1 + x2)) = 0 x(-4 + -4x2 + (1 * x2 + x2 * x2)) = 0 x(-4 + -4x2 + (1x2 + x4)) = 0 Combine like terms: -4x2 + 1x2 = -3x2 x(-4 + -3x2 + x4) = 0 (-4 * x + -3x2 * x + x4 * x) = 0 (-4x + -3x3 + x5) = 0 Solving -4x + -3x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + -3x2 + x4) = 0 Factor a trinomial. x((-1 + -1x2)(4 + -1x2)) = 0 Factor a difference between two squares. x((-1 + -1x2)((2 + x)(2 + -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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 4
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0, -2, 2}
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