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Simplifying x(x + 1)(x + -1) = 0 Reorder the terms: x(1 + x)(x + -1) = 0 Reorder the terms: x(1 + x)(-1 + x) = 0 Multiply (1 + x) * (-1 + x) x(1(-1 + x) + x(-1 + x)) = 0 x((-1 * 1 + x * 1) + x(-1 + x)) = 0 x((-1 + 1x) + x(-1 + x)) = 0 x(-1 + 1x + (-1 * x + x * x)) = 0 x(-1 + 1x + (-1x + x2)) = 0 Combine like terms: 1x + -1x = 0 x(-1 + 0 + x2) = 0 x(-1 + x2) = 0 (-1 * x + x2 * x) = 0 (-1x + x3) = 0 Solving -1x + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + x2) = 0 Factor a difference between two squares. x((1 + x)(-1 + x)) = 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 + 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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