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Simplifying (x + -1)(x + -1)(x + -1) + -1x + 1 = 0 Reorder the terms: (-1 + x)(x + -1)(x + -1) + -1x + 1 = 0 Reorder the terms: (-1 + x)(-1 + x)(x + -1) + -1x + 1 = 0 Reorder the terms: (-1 + x)(-1 + x)(-1 + x) + -1x + 1 = 0 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x))(-1 + x) + -1x + 1 = 0 ((-1 * -1 + x * -1) + x(-1 + x))(-1 + x) + -1x + 1 = 0 ((1 + -1x) + x(-1 + x))(-1 + x) + -1x + 1 = 0 (1 + -1x + (-1 * x + x * x))(-1 + x) + -1x + 1 = 0 (1 + -1x + (-1x + x2))(-1 + x) + -1x + 1 = 0 Combine like terms: -1x + -1x = -2x (1 + -2x + x2)(-1 + x) + -1x + 1 = 0 Multiply (1 + -2x + x2) * (-1 + x) (1(-1 + x) + -2x * (-1 + x) + x2(-1 + x)) + -1x + 1 = 0 ((-1 * 1 + x * 1) + -2x * (-1 + x) + x2(-1 + x)) + -1x + 1 = 0 ((-1 + 1x) + -2x * (-1 + x) + x2(-1 + x)) + -1x + 1 = 0 (-1 + 1x + (-1 * -2x + x * -2x) + x2(-1 + x)) + -1x + 1 = 0 (-1 + 1x + (2x + -2x2) + x2(-1 + x)) + -1x + 1 = 0 (-1 + 1x + 2x + -2x2 + (-1 * x2 + x * x2)) + -1x + 1 = 0 (-1 + 1x + 2x + -2x2 + (-1x2 + x3)) + -1x + 1 = 0 Combine like terms: 1x + 2x = 3x (-1 + 3x + -2x2 + -1x2 + x3) + -1x + 1 = 0 Combine like terms: -2x2 + -1x2 = -3x2 (-1 + 3x + -3x2 + x3) + -1x + 1 = 0 Reorder the terms: -1 + 1 + 3x + -1x + -3x2 + x3 = 0 Combine like terms: -1 + 1 = 0 0 + 3x + -1x + -3x2 + x3 = 0 3x + -1x + -3x2 + x3 = 0 Combine like terms: 3x + -1x = 2x 2x + -3x2 + x3 = 0 Solving 2x + -3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + -3x + x2) = 0 Factor a trinomial. x((1 + -1x)(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 + -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 3
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, 2}
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