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Simplifying (4x3 + -12x) + (-2x3 + 10x) = 0 Reorder the terms: (-12x + 4x3) + (-2x3 + 10x) = 0 Remove parenthesis around (-12x + 4x3) -12x + 4x3 + (-2x3 + 10x) = 0 Reorder the terms: -12x + 4x3 + (10x + -2x3) = 0 Remove parenthesis around (10x + -2x3) -12x + 4x3 + 10x + -2x3 = 0 Reorder the terms: -12x + 10x + 4x3 + -2x3 = 0 Combine like terms: -12x + 10x = -2x -2x + 4x3 + -2x3 = 0 Combine like terms: 4x3 + -2x3 = 2x3 -2x + 2x3 = 0 Solving -2x + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1 + x2) = 0 Factor a difference between two squares. 2x((1 + x)(-1 + x)) = 0 Ignore the factor 2.Subproblem 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 + 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 = 1Solution
x = {0, -1, 1}
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