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Simplifying (x + -7)(x + -5) + (x + -8)(x + -6) = x + 128 Reorder the terms: (-7 + x)(x + -5) + (x + -8)(x + -6) = x + 128 Reorder the terms: (-7 + x)(-5 + x) + (x + -8)(x + -6) = x + 128 Multiply (-7 + x) * (-5 + x) (-7(-5 + x) + x(-5 + x)) + (x + -8)(x + -6) = x + 128 ((-5 * -7 + x * -7) + x(-5 + x)) + (x + -8)(x + -6) = x + 128 ((35 + -7x) + x(-5 + x)) + (x + -8)(x + -6) = x + 128 (35 + -7x + (-5 * x + x * x)) + (x + -8)(x + -6) = x + 128 (35 + -7x + (-5x + x2)) + (x + -8)(x + -6) = x + 128 Combine like terms: -7x + -5x = -12x (35 + -12x + x2) + (x + -8)(x + -6) = x + 128 Reorder the terms: 35 + -12x + x2 + (-8 + x)(x + -6) = x + 128 Reorder the terms: 35 + -12x + x2 + (-8 + x)(-6 + x) = x + 128 Multiply (-8 + x) * (-6 + x) 35 + -12x + x2 + (-8(-6 + x) + x(-6 + x)) = x + 128 35 + -12x + x2 + ((-6 * -8 + x * -8) + x(-6 + x)) = x + 128 35 + -12x + x2 + ((48 + -8x) + x(-6 + x)) = x + 128 35 + -12x + x2 + (48 + -8x + (-6 * x + x * x)) = x + 128 35 + -12x + x2 + (48 + -8x + (-6x + x2)) = x + 128 Combine like terms: -8x + -6x = -14x 35 + -12x + x2 + (48 + -14x + x2) = x + 128 Reorder the terms: 35 + 48 + -12x + -14x + x2 + x2 = x + 128 Combine like terms: 35 + 48 = 83 83 + -12x + -14x + x2 + x2 = x + 128 Combine like terms: -12x + -14x = -26x 83 + -26x + x2 + x2 = x + 128 Combine like terms: x2 + x2 = 2x2 83 + -26x + 2x2 = x + 128 Reorder the terms: 83 + -26x + 2x2 = 128 + x Solving 83 + -26x + 2x2 = 128 + x Solving for variable 'x'. Reorder the terms: 83 + -128 + -26x + -1x + 2x2 = 128 + x + -128 + -1x Combine like terms: 83 + -128 = -45 -45 + -26x + -1x + 2x2 = 128 + x + -128 + -1x Combine like terms: -26x + -1x = -27x -45 + -27x + 2x2 = 128 + x + -128 + -1x Reorder the terms: -45 + -27x + 2x2 = 128 + -128 + x + -1x Combine like terms: 128 + -128 = 0 -45 + -27x + 2x2 = 0 + x + -1x -45 + -27x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -45 + -27x + 2x2 = 0 Factor a trinomial. (-3 + -2x)(15 + -1x) = 0Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {-1.5, 15}
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