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Simplifying (x + 1)(x + -1) = x(4x + -3) + -1 Reorder the terms: (1 + x)(x + -1) = x(4x + -3) + -1 Reorder the terms: (1 + x)(-1 + x) = x(4x + -3) + -1 Multiply (1 + x) * (-1 + x) (1(-1 + x) + x(-1 + x)) = x(4x + -3) + -1 ((-1 * 1 + x * 1) + x(-1 + x)) = x(4x + -3) + -1 ((-1 + 1x) + x(-1 + x)) = x(4x + -3) + -1 (-1 + 1x + (-1 * x + x * x)) = x(4x + -3) + -1 (-1 + 1x + (-1x + x2)) = x(4x + -3) + -1 Combine like terms: 1x + -1x = 0 (-1 + 0 + x2) = x(4x + -3) + -1 (-1 + x2) = x(4x + -3) + -1 Reorder the terms: -1 + x2 = x(-3 + 4x) + -1 -1 + x2 = (-3 * x + 4x * x) + -1 -1 + x2 = (-3x + 4x2) + -1 Reorder the terms: -1 + x2 = -1 + -3x + 4x2 Add '1' to each side of the equation. -1 + 1 + x2 = -1 + -3x + 1 + 4x2 Combine like terms: -1 + 1 = 0 0 + x2 = -1 + -3x + 1 + 4x2 x2 = -1 + -3x + 1 + 4x2 Reorder the terms: x2 = -1 + 1 + -3x + 4x2 Combine like terms: -1 + 1 = 0 x2 = 0 + -3x + 4x2 x2 = -3x + 4x2 Solving x2 = -3x + 4x2 Solving for variable 'x'. Reorder the terms: 3x + x2 + -4x2 = -3x + 4x2 + 3x + -4x2 Combine like terms: x2 + -4x2 = -3x2 3x + -3x2 = -3x + 4x2 + 3x + -4x2 Reorder the terms: 3x + -3x2 = -3x + 3x + 4x2 + -4x2 Combine like terms: -3x + 3x = 0 3x + -3x2 = 0 + 4x2 + -4x2 3x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 3x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(1 + -1x) = 0 Ignore the factor 3.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 + -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, 1}
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