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Simplifying (3x + 2)(x + 1) = (x + -2)(2x + 3) Reorder the terms: (2 + 3x)(x + 1) = (x + -2)(2x + 3) Reorder the terms: (2 + 3x)(1 + x) = (x + -2)(2x + 3) Multiply (2 + 3x) * (1 + x) (2(1 + x) + 3x * (1 + x)) = (x + -2)(2x + 3) ((1 * 2 + x * 2) + 3x * (1 + x)) = (x + -2)(2x + 3) ((2 + 2x) + 3x * (1 + x)) = (x + -2)(2x + 3) (2 + 2x + (1 * 3x + x * 3x)) = (x + -2)(2x + 3) (2 + 2x + (3x + 3x2)) = (x + -2)(2x + 3) Combine like terms: 2x + 3x = 5x (2 + 5x + 3x2) = (x + -2)(2x + 3) Reorder the terms: 2 + 5x + 3x2 = (-2 + x)(2x + 3) Reorder the terms: 2 + 5x + 3x2 = (-2 + x)(3 + 2x) Multiply (-2 + x) * (3 + 2x) 2 + 5x + 3x2 = (-2(3 + 2x) + x(3 + 2x)) 2 + 5x + 3x2 = ((3 * -2 + 2x * -2) + x(3 + 2x)) 2 + 5x + 3x2 = ((-6 + -4x) + x(3 + 2x)) 2 + 5x + 3x2 = (-6 + -4x + (3 * x + 2x * x)) 2 + 5x + 3x2 = (-6 + -4x + (3x + 2x2)) Combine like terms: -4x + 3x = -1x 2 + 5x + 3x2 = (-6 + -1x + 2x2) Solving 2 + 5x + 3x2 = -6 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: 2 + 6 + 5x + x + 3x2 + -2x2 = -6 + -1x + 2x2 + 6 + x + -2x2 Combine like terms: 2 + 6 = 8 8 + 5x + x + 3x2 + -2x2 = -6 + -1x + 2x2 + 6 + x + -2x2 Combine like terms: 5x + x = 6x 8 + 6x + 3x2 + -2x2 = -6 + -1x + 2x2 + 6 + x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 8 + 6x + 1x2 = -6 + -1x + 2x2 + 6 + x + -2x2 Reorder the terms: 8 + 6x + 1x2 = -6 + 6 + -1x + x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 8 + 6x + 1x2 = 0 + -1x + x + 2x2 + -2x2 8 + 6x + 1x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 8 + 6x + 1x2 = 0 + 2x2 + -2x2 8 + 6x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + 6x + 1x2 = 0 Factor a trinomial. (4 + x)(2 + x) = 0Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-4, -2}
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