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Simplifying (x + 5)(x + 7) = 8 Reorder the terms: (5 + x)(x + 7) = 8 Reorder the terms: (5 + x)(7 + x) = 8 Multiply (5 + x) * (7 + x) (5(7 + x) + x(7 + x)) = 8 ((7 * 5 + x * 5) + x(7 + x)) = 8 ((35 + 5x) + x(7 + x)) = 8 (35 + 5x + (7 * x + x * x)) = 8 (35 + 5x + (7x + x^{2})) = 8 Combine like terms: 5x + 7x = 12x (35 + 12x + x^{2}) = 8 Solving 35 + 12x + x^{2}= 8 Solving for variable 'x'. Reorder the terms: 35 + -8 + 12x + x^{2}= 8 + -8 Combine like terms: 35 + -8 = 27 27 + 12x + x^{2}= 8 + -8 Combine like terms: 8 + -8 = 0 27 + 12x + x^{2}= 0 Factor a trinomial. (9 + x)(3 + x) = 0## Subproblem 1

Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9## Subproblem 2

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 = -3## Solution

x = {-9, -3}

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