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Simplifying (n + 2)(n + 5) = 70 Reorder the terms: (2 + n)(n + 5) = 70 Reorder the terms: (2 + n)(5 + n) = 70 Multiply (2 + n) * (5 + n) (2(5 + n) + n(5 + n)) = 70 ((5 * 2 + n * 2) + n(5 + n)) = 70 ((10 + 2n) + n(5 + n)) = 70 (10 + 2n + (5 * n + n * n)) = 70 (10 + 2n + (5n + n2)) = 70 Combine like terms: 2n + 5n = 7n (10 + 7n + n2) = 70 Solving 10 + 7n + n2 = 70 Solving for variable 'n'. Reorder the terms: 10 + -70 + 7n + n2 = 70 + -70 Combine like terms: 10 + -70 = -60 -60 + 7n + n2 = 70 + -70 Combine like terms: 70 + -70 = 0 -60 + 7n + n2 = 0 Factor a trinomial. (-12 + -1n)(5 + -1n) = 0Subproblem 1
Set the factor '(-12 + -1n)' equal to zero and attempt to solve: Simplifying -12 + -1n = 0 Solving -12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1n = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1n = 0 + 12 -1n = 0 + 12 Combine like terms: 0 + 12 = 12 -1n = 12 Divide each side by '-1'. n = -12 Simplifying n = -12Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-12, 5}
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