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