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Simplifying (x + 5)(x + 6) = 12 Reorder the terms: (5 + x)(x + 6) = 12 Reorder the terms: (5 + x)(6 + x) = 12 Multiply (5 + x) * (6 + x) (5(6 + x) + x(6 + x)) = 12 ((6 * 5 + x * 5) + x(6 + x)) = 12 ((30 + 5x) + x(6 + x)) = 12 (30 + 5x + (6 * x + x * x)) = 12 (30 + 5x + (6x + x2)) = 12 Combine like terms: 5x + 6x = 11x (30 + 11x + x2) = 12 Solving 30 + 11x + x2 = 12 Solving for variable 'x'. Reorder the terms: 30 + -12 + 11x + x2 = 12 + -12 Combine like terms: 30 + -12 = 18 18 + 11x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 18 + 11x + x2 = 0 Factor a trinomial. (9 + x)(2 + x) = 0Subproblem 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 = -9Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-9, -2}
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