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Simplifying (x + -1)(x + 2) + -1(x + 2)(3x + 8) = 0 Reorder the terms: (-1 + x)(x + 2) + -1(x + 2)(3x + 8) = 0 Reorder the terms: (-1 + x)(2 + x) + -1(x + 2)(3x + 8) = 0 Multiply (-1 + x) * (2 + x) (-1(2 + x) + x(2 + x)) + -1(x + 2)(3x + 8) = 0 ((2 * -1 + x * -1) + x(2 + x)) + -1(x + 2)(3x + 8) = 0 ((-2 + -1x) + x(2 + x)) + -1(x + 2)(3x + 8) = 0 (-2 + -1x + (2 * x + x * x)) + -1(x + 2)(3x + 8) = 0 (-2 + -1x + (2x + x2)) + -1(x + 2)(3x + 8) = 0 Combine like terms: -1x + 2x = 1x (-2 + 1x + x2) + -1(x + 2)(3x + 8) = 0 Reorder the terms: -2 + 1x + x2 + -1(2 + x)(3x + 8) = 0 Reorder the terms: -2 + 1x + x2 + -1(2 + x)(8 + 3x) = 0 Multiply (2 + x) * (8 + 3x) -2 + 1x + x2 + -1(2(8 + 3x) + x(8 + 3x)) = 0 -2 + 1x + x2 + -1((8 * 2 + 3x * 2) + x(8 + 3x)) = 0 -2 + 1x + x2 + -1((16 + 6x) + x(8 + 3x)) = 0 -2 + 1x + x2 + -1(16 + 6x + (8 * x + 3x * x)) = 0 -2 + 1x + x2 + -1(16 + 6x + (8x + 3x2)) = 0 Combine like terms: 6x + 8x = 14x -2 + 1x + x2 + -1(16 + 14x + 3x2) = 0 -2 + 1x + x2 + (16 * -1 + 14x * -1 + 3x2 * -1) = 0 -2 + 1x + x2 + (-16 + -14x + -3x2) = 0 Reorder the terms: -2 + -16 + 1x + -14x + x2 + -3x2 = 0 Combine like terms: -2 + -16 = -18 -18 + 1x + -14x + x2 + -3x2 = 0 Combine like terms: 1x + -14x = -13x -18 + -13x + x2 + -3x2 = 0 Combine like terms: x2 + -3x2 = -2x2 -18 + -13x + -2x2 = 0 Solving -18 + -13x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(18 + 13x + 2x2) = 0 Factor a trinomial. -1((9 + 2x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Subproblem 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 = {-4.5, -2}
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