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Simplifying (x + 7)(x + 5) = 3 Reorder the terms: (7 + x)(x + 5) = 3 Reorder the terms: (7 + x)(5 + x) = 3 Multiply (7 + x) * (5 + x) (7(5 + x) + x(5 + x)) = 3 ((5 * 7 + x * 7) + x(5 + x)) = 3 ((35 + 7x) + x(5 + x)) = 3 (35 + 7x + (5 * x + x * x)) = 3 (35 + 7x + (5x + x2)) = 3 Combine like terms: 7x + 5x = 12x (35 + 12x + x2) = 3 Solving 35 + 12x + x2 = 3 Solving for variable 'x'. Reorder the terms: 35 + -3 + 12x + x2 = 3 + -3 Combine like terms: 35 + -3 = 32 32 + 12x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 32 + 12x + x2 = 0 Factor a trinomial. (8 + x)(4 + x) = 0Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-8, -4}
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