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Simplifying (x + 2)(x + -1) + (x + 5)(x + -3) = -8 Reorder the terms: (2 + x)(x + -1) + (x + 5)(x + -3) = -8 Reorder the terms: (2 + x)(-1 + x) + (x + 5)(x + -3) = -8 Multiply (2 + x) * (-1 + x) (2(-1 + x) + x(-1 + x)) + (x + 5)(x + -3) = -8 ((-1 * 2 + x * 2) + x(-1 + x)) + (x + 5)(x + -3) = -8 ((-2 + 2x) + x(-1 + x)) + (x + 5)(x + -3) = -8 (-2 + 2x + (-1 * x + x * x)) + (x + 5)(x + -3) = -8 (-2 + 2x + (-1x + x2)) + (x + 5)(x + -3) = -8 Combine like terms: 2x + -1x = 1x (-2 + 1x + x2) + (x + 5)(x + -3) = -8 Reorder the terms: -2 + 1x + x2 + (5 + x)(x + -3) = -8 Reorder the terms: -2 + 1x + x2 + (5 + x)(-3 + x) = -8 Multiply (5 + x) * (-3 + x) -2 + 1x + x2 + (5(-3 + x) + x(-3 + x)) = -8 -2 + 1x + x2 + ((-3 * 5 + x * 5) + x(-3 + x)) = -8 -2 + 1x + x2 + ((-15 + 5x) + x(-3 + x)) = -8 -2 + 1x + x2 + (-15 + 5x + (-3 * x + x * x)) = -8 -2 + 1x + x2 + (-15 + 5x + (-3x + x2)) = -8 Combine like terms: 5x + -3x = 2x -2 + 1x + x2 + (-15 + 2x + x2) = -8 Reorder the terms: -2 + -15 + 1x + 2x + x2 + x2 = -8 Combine like terms: -2 + -15 = -17 -17 + 1x + 2x + x2 + x2 = -8 Combine like terms: 1x + 2x = 3x -17 + 3x + x2 + x2 = -8 Combine like terms: x2 + x2 = 2x2 -17 + 3x + 2x2 = -8 Solving -17 + 3x + 2x2 = -8 Solving for variable 'x'. Reorder the terms: -17 + 8 + 3x + 2x2 = -8 + 8 Combine like terms: -17 + 8 = -9 -9 + 3x + 2x2 = -8 + 8 Combine like terms: -8 + 8 = 0 -9 + 3x + 2x2 = 0 Factor a trinomial. (-3 + -1x)(3 + -2x) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-3, 1.5}
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