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