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Simplifying 0 = -1x5 + 5x3 + -4x Reorder the terms: 0 = -4x + 5x3 + -1x5 Solving 0 = -4x + 5x3 + -1x5 Solving for variable 'x'. Remove the zero: 4x + -5x3 + x5 = -4x + 5x3 + -1x5 + 4x + -5x3 + x5 Reorder the terms: 4x + -5x3 + x5 = -4x + 4x + 5x3 + -5x3 + -1x5 + x5 Combine like terms: -4x + 4x = 0 4x + -5x3 + x5 = 0 + 5x3 + -5x3 + -1x5 + x5 4x + -5x3 + x5 = 5x3 + -5x3 + -1x5 + x5 Combine like terms: 5x3 + -5x3 = 0 4x + -5x3 + x5 = 0 + -1x5 + x5 4x + -5x3 + x5 = -1x5 + x5 Combine like terms: -1x5 + x5 = 0 4x + -5x3 + x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -5x2 + x4) = 0 Factor a trinomial. x((1 + -1x2)(4 + -1x2)) = 0 Factor a difference between two squares. x(((1 + x)(1 + -1x))(4 + -1x2)) = 0 Factor a difference between two squares. x(((2 + x)(2 + -1x))(1 + x)(1 + -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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 4
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 5
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, -1, 1, -2, 2}
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