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Simplifying (2x + 3)(x + 1) = (x + 2)(x + -1) + 2 Reorder the terms: (3 + 2x)(x + 1) = (x + 2)(x + -1) + 2 Reorder the terms: (3 + 2x)(1 + x) = (x + 2)(x + -1) + 2 Multiply (3 + 2x) * (1 + x) (3(1 + x) + 2x * (1 + x)) = (x + 2)(x + -1) + 2 ((1 * 3 + x * 3) + 2x * (1 + x)) = (x + 2)(x + -1) + 2 ((3 + 3x) + 2x * (1 + x)) = (x + 2)(x + -1) + 2 (3 + 3x + (1 * 2x + x * 2x)) = (x + 2)(x + -1) + 2 (3 + 3x + (2x + 2x2)) = (x + 2)(x + -1) + 2 Combine like terms: 3x + 2x = 5x (3 + 5x + 2x2) = (x + 2)(x + -1) + 2 Reorder the terms: 3 + 5x + 2x2 = (2 + x)(x + -1) + 2 Reorder the terms: 3 + 5x + 2x2 = (2 + x)(-1 + x) + 2 Multiply (2 + x) * (-1 + x) 3 + 5x + 2x2 = (2(-1 + x) + x(-1 + x)) + 2 3 + 5x + 2x2 = ((-1 * 2 + x * 2) + x(-1 + x)) + 2 3 + 5x + 2x2 = ((-2 + 2x) + x(-1 + x)) + 2 3 + 5x + 2x2 = (-2 + 2x + (-1 * x + x * x)) + 2 3 + 5x + 2x2 = (-2 + 2x + (-1x + x2)) + 2 Combine like terms: 2x + -1x = 1x 3 + 5x + 2x2 = (-2 + 1x + x2) + 2 Reorder the terms: 3 + 5x + 2x2 = -2 + 2 + 1x + x2 Combine like terms: -2 + 2 = 0 3 + 5x + 2x2 = 0 + 1x + x2 3 + 5x + 2x2 = 1x + x2 Solving 3 + 5x + 2x2 = 1x + x2 Solving for variable 'x'. Reorder the terms: 3 + 5x + -1x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: 5x + -1x = 4x 3 + 4x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 3 + 4x + 1x2 = 1x + x2 + -1x + -1x2 Reorder the terms: 3 + 4x + 1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 3 + 4x + 1x2 = 0 + x2 + -1x2 3 + 4x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3 + 4x + 1x2 = 0 Factor a trinomial. (3 + x)(1 + x) = 0Subproblem 1
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 = -3Subproblem 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 = -1Solution
x = {-3, -1}
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