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