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Simplifying (3x + 8)(8 + -2x) + (x + 4)(2x + 7) = (x + 4)(3x + 8) * 13 Reorder the terms: (8 + 3x)(8 + -2x) + (x + 4)(2x + 7) = (x + 4)(3x + 8) * 13 Multiply (8 + 3x) * (8 + -2x) (8(8 + -2x) + 3x * (8 + -2x)) + (x + 4)(2x + 7) = (x + 4)(3x + 8) * 13 ((8 * 8 + -2x * 8) + 3x * (8 + -2x)) + (x + 4)(2x + 7) = (x + 4)(3x + 8) * 13 ((64 + -16x) + 3x * (8 + -2x)) + (x + 4)(2x + 7) = (x + 4)(3x + 8) * 13 (64 + -16x + (8 * 3x + -2x * 3x)) + (x + 4)(2x + 7) = (x + 4)(3x + 8) * 13 (64 + -16x + (24x + -6x2)) + (x + 4)(2x + 7) = (x + 4)(3x + 8) * 13 Combine like terms: -16x + 24x = 8x (64 + 8x + -6x2) + (x + 4)(2x + 7) = (x + 4)(3x + 8) * 13 Reorder the terms: 64 + 8x + -6x2 + (4 + x)(2x + 7) = (x + 4)(3x + 8) * 13 Reorder the terms: 64 + 8x + -6x2 + (4 + x)(7 + 2x) = (x + 4)(3x + 8) * 13 Multiply (4 + x) * (7 + 2x) 64 + 8x + -6x2 + (4(7 + 2x) + x(7 + 2x)) = (x + 4)(3x + 8) * 13 64 + 8x + -6x2 + ((7 * 4 + 2x * 4) + x(7 + 2x)) = (x + 4)(3x + 8) * 13 64 + 8x + -6x2 + ((28 + 8x) + x(7 + 2x)) = (x + 4)(3x + 8) * 13 64 + 8x + -6x2 + (28 + 8x + (7 * x + 2x * x)) = (x + 4)(3x + 8) * 13 64 + 8x + -6x2 + (28 + 8x + (7x + 2x2)) = (x + 4)(3x + 8) * 13 Combine like terms: 8x + 7x = 15x 64 + 8x + -6x2 + (28 + 15x + 2x2) = (x + 4)(3x + 8) * 13 Reorder the terms: 64 + 28 + 8x + 15x + -6x2 + 2x2 = (x + 4)(3x + 8) * 13 Combine like terms: 64 + 28 = 92 92 + 8x + 15x + -6x2 + 2x2 = (x + 4)(3x + 8) * 13 Combine like terms: 8x + 15x = 23x 92 + 23x + -6x2 + 2x2 = (x + 4)(3x + 8) * 13 Combine like terms: -6x2 + 2x2 = -4x2 92 + 23x + -4x2 = (x + 4)(3x + 8) * 13 Reorder the terms: 92 + 23x + -4x2 = (4 + x)(3x + 8) * 13 Reorder the terms: 92 + 23x + -4x2 = (4 + x)(8 + 3x) * 13 Reorder the terms for easier multiplication: 92 + 23x + -4x2 = 13(4 + x)(8 + 3x) Multiply (4 + x) * (8 + 3x) 92 + 23x + -4x2 = 13(4(8 + 3x) + x(8 + 3x)) 92 + 23x + -4x2 = 13((8 * 4 + 3x * 4) + x(8 + 3x)) 92 + 23x + -4x2 = 13((32 + 12x) + x(8 + 3x)) 92 + 23x + -4x2 = 13(32 + 12x + (8 * x + 3x * x)) 92 + 23x + -4x2 = 13(32 + 12x + (8x + 3x2)) Combine like terms: 12x + 8x = 20x 92 + 23x + -4x2 = 13(32 + 20x + 3x2) 92 + 23x + -4x2 = (32 * 13 + 20x * 13 + 3x2 * 13) 92 + 23x + -4x2 = (416 + 260x + 39x2) Solving 92 + 23x + -4x2 = 416 + 260x + 39x2 Solving for variable 'x'. Reorder the terms: 92 + -416 + 23x + -260x + -4x2 + -39x2 = 416 + 260x + 39x2 + -416 + -260x + -39x2 Combine like terms: 92 + -416 = -324 -324 + 23x + -260x + -4x2 + -39x2 = 416 + 260x + 39x2 + -416 + -260x + -39x2 Combine like terms: 23x + -260x = -237x -324 + -237x + -4x2 + -39x2 = 416 + 260x + 39x2 + -416 + -260x + -39x2 Combine like terms: -4x2 + -39x2 = -43x2 -324 + -237x + -43x2 = 416 + 260x + 39x2 + -416 + -260x + -39x2 Reorder the terms: -324 + -237x + -43x2 = 416 + -416 + 260x + -260x + 39x2 + -39x2 Combine like terms: 416 + -416 = 0 -324 + -237x + -43x2 = 0 + 260x + -260x + 39x2 + -39x2 -324 + -237x + -43x2 = 260x + -260x + 39x2 + -39x2 Combine like terms: 260x + -260x = 0 -324 + -237x + -43x2 = 0 + 39x2 + -39x2 -324 + -237x + -43x2 = 39x2 + -39x2 Combine like terms: 39x2 + -39x2 = 0 -324 + -237x + -43x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(324 + 237x + 43x2) = 0 Factor a trinomial. -1((3 + x)(108 + 43x)) = 0 Ignore the factor -1.Subproblem 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 '(108 + 43x)' equal to zero and attempt to solve: Simplifying 108 + 43x = 0 Solving 108 + 43x = 0 Move all terms containing x to the left, all other terms to the right. Add '-108' to each side of the equation. 108 + -108 + 43x = 0 + -108 Combine like terms: 108 + -108 = 0 0 + 43x = 0 + -108 43x = 0 + -108 Combine like terms: 0 + -108 = -108 43x = -108 Divide each side by '43'. x = -2.511627907 Simplifying x = -2.511627907Solution
x = {-3, -2.511627907}
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