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Simplifying (x + 3)(x + 4) = 132 Reorder the terms: (3 + x)(x + 4) = 132 Reorder the terms: (3 + x)(4 + x) = 132 Multiply (3 + x) * (4 + x) (3(4 + x) + x(4 + x)) = 132 ((4 * 3 + x * 3) + x(4 + x)) = 132 ((12 + 3x) + x(4 + x)) = 132 (12 + 3x + (4 * x + x * x)) = 132 (12 + 3x + (4x + x2)) = 132 Combine like terms: 3x + 4x = 7x (12 + 7x + x2) = 132 Solving 12 + 7x + x2 = 132 Solving for variable 'x'. Reorder the terms: 12 + -132 + 7x + x2 = 132 + -132 Combine like terms: 12 + -132 = -120 -120 + 7x + x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -120 + 7x + x2 = 0 Factor a trinomial. (-15 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 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 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-15, 8}
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