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Simplifying (4x + 7)(3x + 4) = (x + 2)(x + 4) Reorder the terms: (7 + 4x)(3x + 4) = (x + 2)(x + 4) Reorder the terms: (7 + 4x)(4 + 3x) = (x + 2)(x + 4) Multiply (7 + 4x) * (4 + 3x) (7(4 + 3x) + 4x * (4 + 3x)) = (x + 2)(x + 4) ((4 * 7 + 3x * 7) + 4x * (4 + 3x)) = (x + 2)(x + 4) ((28 + 21x) + 4x * (4 + 3x)) = (x + 2)(x + 4) (28 + 21x + (4 * 4x + 3x * 4x)) = (x + 2)(x + 4) (28 + 21x + (16x + 12x2)) = (x + 2)(x + 4) Combine like terms: 21x + 16x = 37x (28 + 37x + 12x2) = (x + 2)(x + 4) Reorder the terms: 28 + 37x + 12x2 = (2 + x)(x + 4) Reorder the terms: 28 + 37x + 12x2 = (2 + x)(4 + x) Multiply (2 + x) * (4 + x) 28 + 37x + 12x2 = (2(4 + x) + x(4 + x)) 28 + 37x + 12x2 = ((4 * 2 + x * 2) + x(4 + x)) 28 + 37x + 12x2 = ((8 + 2x) + x(4 + x)) 28 + 37x + 12x2 = (8 + 2x + (4 * x + x * x)) 28 + 37x + 12x2 = (8 + 2x + (4x + x2)) Combine like terms: 2x + 4x = 6x 28 + 37x + 12x2 = (8 + 6x + x2) Solving 28 + 37x + 12x2 = 8 + 6x + x2 Solving for variable 'x'. Reorder the terms: 28 + -8 + 37x + -6x + 12x2 + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2 Combine like terms: 28 + -8 = 20 20 + 37x + -6x + 12x2 + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2 Combine like terms: 37x + -6x = 31x 20 + 31x + 12x2 + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2 Combine like terms: 12x2 + -1x2 = 11x2 20 + 31x + 11x2 = 8 + 6x + x2 + -8 + -6x + -1x2 Reorder the terms: 20 + 31x + 11x2 = 8 + -8 + 6x + -6x + x2 + -1x2 Combine like terms: 8 + -8 = 0 20 + 31x + 11x2 = 0 + 6x + -6x + x2 + -1x2 20 + 31x + 11x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 20 + 31x + 11x2 = 0 + x2 + -1x2 20 + 31x + 11x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 20 + 31x + 11x2 = 0 Factor a trinomial. (20 + 11x)(1 + x) = 0Subproblem 1
Set the factor '(20 + 11x)' equal to zero and attempt to solve: Simplifying 20 + 11x = 0 Solving 20 + 11x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + 11x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 11x = 0 + -20 11x = 0 + -20 Combine like terms: 0 + -20 = -20 11x = -20 Divide each side by '11'. x = -1.818181818 Simplifying x = -1.818181818Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-1.818181818, -1}
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