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Simplifying (x + 1)(x + 1)(x + -1)(x + -1) = 0 Reorder the terms: (1 + x)(x + 1)(x + -1)(x + -1) = 0 Reorder the terms: (1 + x)(1 + x)(x + -1)(x + -1) = 0 Reorder the terms: (1 + x)(1 + x)(-1 + x)(x + -1) = 0 Reorder the terms: (1 + x)(1 + x)(-1 + x)(-1 + x) = 0 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x))(-1 + x)(-1 + x) = 0 ((1 * 1 + x * 1) + x(1 + x))(-1 + x)(-1 + x) = 0 ((1 + 1x) + x(1 + x))(-1 + x)(-1 + x) = 0 (1 + 1x + (1 * x + x * x))(-1 + x)(-1 + x) = 0 (1 + 1x + (1x + x2))(-1 + x)(-1 + x) = 0 Combine like terms: 1x + 1x = 2x (1 + 2x + x2)(-1 + x)(-1 + x) = 0 Multiply (1 + 2x + x2) * (-1 + x) (1(-1 + x) + 2x * (-1 + x) + x2(-1 + x))(-1 + x) = 0 ((-1 * 1 + x * 1) + 2x * (-1 + x) + x2(-1 + x))(-1 + x) = 0 ((-1 + 1x) + 2x * (-1 + x) + x2(-1 + x))(-1 + x) = 0 (-1 + 1x + (-1 * 2x + x * 2x) + x2(-1 + x))(-1 + x) = 0 (-1 + 1x + (-2x + 2x2) + x2(-1 + x))(-1 + x) = 0 (-1 + 1x + -2x + 2x2 + (-1 * x2 + x * x2))(-1 + x) = 0 (-1 + 1x + -2x + 2x2 + (-1x2 + x3))(-1 + x) = 0 Combine like terms: 1x + -2x = -1x (-1 + -1x + 2x2 + -1x2 + x3)(-1 + x) = 0 Combine like terms: 2x2 + -1x2 = 1x2 (-1 + -1x + 1x2 + x3)(-1 + x) = 0 Multiply (-1 + -1x + 1x2 + x3) * (-1 + x) (-1(-1 + x) + -1x * (-1 + x) + 1x2 * (-1 + x) + x3(-1 + x)) = 0 ((-1 * -1 + x * -1) + -1x * (-1 + x) + 1x2 * (-1 + x) + x3(-1 + x)) = 0 ((1 + -1x) + -1x * (-1 + x) + 1x2 * (-1 + x) + x3(-1 + x)) = 0 (1 + -1x + (-1 * -1x + x * -1x) + 1x2 * (-1 + x) + x3(-1 + x)) = 0 (1 + -1x + (1x + -1x2) + 1x2 * (-1 + x) + x3(-1 + x)) = 0 (1 + -1x + 1x + -1x2 + (-1 * 1x2 + x * 1x2) + x3(-1 + x)) = 0 (1 + -1x + 1x + -1x2 + (-1x2 + 1x3) + x3(-1 + x)) = 0 (1 + -1x + 1x + -1x2 + -1x2 + 1x3 + (-1 * x3 + x * x3)) = 0 (1 + -1x + 1x + -1x2 + -1x2 + 1x3 + (-1x3 + x4)) = 0 Combine like terms: -1x + 1x = 0 (1 + 0 + -1x2 + -1x2 + 1x3 + -1x3 + x4) = 0 (1 + -1x2 + -1x2 + 1x3 + -1x3 + x4) = 0 Combine like terms: -1x2 + -1x2 = -2x2 (1 + -2x2 + 1x3 + -1x3 + x4) = 0 Combine like terms: 1x3 + -1x3 = 0 (1 + -2x2 + 0 + x4) = 0 (1 + -2x2 + x4) = 0 Solving 1 + -2x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x2)(1 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(1 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(1 + x)(1 + -1x) = 0Subproblem 1
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 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 '(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 4
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 = {-1, 1, -1, 1}
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