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Simplifying (x + 12)(x + 8) = 165 Reorder the terms: (12 + x)(x + 8) = 165 Reorder the terms: (12 + x)(8 + x) = 165 Multiply (12 + x) * (8 + x) (12(8 + x) + x(8 + x)) = 165 ((8 * 12 + x * 12) + x(8 + x)) = 165 ((96 + 12x) + x(8 + x)) = 165 (96 + 12x + (8 * x + x * x)) = 165 (96 + 12x + (8x + x2)) = 165 Combine like terms: 12x + 8x = 20x (96 + 20x + x2) = 165 Solving 96 + 20x + x2 = 165 Solving for variable 'x'. Reorder the terms: 96 + -165 + 20x + x2 = 165 + -165 Combine like terms: 96 + -165 = -69 -69 + 20x + x2 = 165 + -165 Combine like terms: 165 + -165 = 0 -69 + 20x + x2 = 0 Factor a trinomial. (-23 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve: Simplifying -23 + -1x = 0 Solving -23 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -1x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1x = 0 + 23 -1x = 0 + 23 Combine like terms: 0 + 23 = 23 -1x = 23 Divide each side by '-1'. x = -23 Simplifying x = -23Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-23, 3}
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