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Simplifying (n + 3)(n + 2) = 42 Reorder the terms: (3 + n)(n + 2) = 42 Reorder the terms: (3 + n)(2 + n) = 42 Multiply (3 + n) * (2 + n) (3(2 + n) + n(2 + n)) = 42 ((2 * 3 + n * 3) + n(2 + n)) = 42 ((6 + 3n) + n(2 + n)) = 42 (6 + 3n + (2 * n + n * n)) = 42 (6 + 3n + (2n + n2)) = 42 Combine like terms: 3n + 2n = 5n (6 + 5n + n2) = 42 Solving 6 + 5n + n2 = 42 Solving for variable 'n'. Reorder the terms: 6 + -42 + 5n + n2 = 42 + -42 Combine like terms: 6 + -42 = -36 -36 + 5n + n2 = 42 + -42 Combine like terms: 42 + -42 = 0 -36 + 5n + n2 = 0 Factor a trinomial. (-9 + -1n)(4 + -1n) = 0Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve: Simplifying -9 + -1n = 0 Solving -9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1n = 0 + 9 -1n = 0 + 9 Combine like terms: 0 + 9 = 9 -1n = 9 Divide each side by '-1'. n = -9 Simplifying n = -9Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {-9, 4}
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