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