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Simplifying (x + -1)(x + 1) + -3x(x + -1) = 0 Reorder the terms: (-1 + x)(x + 1) + -3x(x + -1) = 0 Reorder the terms: (-1 + x)(1 + x) + -3x(x + -1) = 0 Multiply (-1 + x) * (1 + x) (-1(1 + x) + x(1 + x)) + -3x(x + -1) = 0 ((1 * -1 + x * -1) + x(1 + x)) + -3x(x + -1) = 0 ((-1 + -1x) + x(1 + x)) + -3x(x + -1) = 0 (-1 + -1x + (1 * x + x * x)) + -3x(x + -1) = 0 (-1 + -1x + (1x + x2)) + -3x(x + -1) = 0 Combine like terms: -1x + 1x = 0 (-1 + 0 + x2) + -3x(x + -1) = 0 (-1 + x2) + -3x(x + -1) = 0 Reorder the terms: -1 + x2 + -3x(-1 + x) = 0 -1 + x2 + (-1 * -3x + x * -3x) = 0 -1 + x2 + (3x + -3x2) = 0 Reorder the terms: -1 + 3x + x2 + -3x2 = 0 Combine like terms: x2 + -3x2 = -2x2 -1 + 3x + -2x2 = 0 Solving -1 + 3x + -2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + x)(1 + -2x) = 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 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {1, 0.5}
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