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Simplifying (12 + x)(5 + x) = 120 Multiply (12 + x) * (5 + x) (12(5 + x) + x(5 + x)) = 120 ((5 * 12 + x * 12) + x(5 + x)) = 120 ((60 + 12x) + x(5 + x)) = 120 (60 + 12x + (5 * x + x * x)) = 120 (60 + 12x + (5x + x2)) = 120 Combine like terms: 12x + 5x = 17x (60 + 17x + x2) = 120 Solving 60 + 17x + x2 = 120 Solving for variable 'x'. Reorder the terms: 60 + -120 + 17x + x2 = 120 + -120 Combine like terms: 60 + -120 = -60 -60 + 17x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -60 + 17x + x2 = 0 Factor a trinomial. (-20 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve: Simplifying -20 + -1x = 0 Solving -20 + -1x = 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 + -1x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1x = 0 + 20 -1x = 0 + 20 Combine like terms: 0 + 20 = 20 -1x = 20 Divide each side by '-1'. x = -20 Simplifying x = -20Subproblem 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 = {-20, 3}
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