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Simplifying (n + 5)(n + 7) = 0 Reorder the terms: (5 + n)(n + 7) = 0 Reorder the terms: (5 + n)(7 + n) = 0 Multiply (5 + n) * (7 + n) (5(7 + n) + n(7 + n)) = 0 ((7 * 5 + n * 5) + n(7 + n)) = 0 ((35 + 5n) + n(7 + n)) = 0 (35 + 5n + (7 * n + n * n)) = 0 (35 + 5n + (7n + n2)) = 0 Combine like terms: 5n + 7n = 12n (35 + 12n + n2) = 0 Solving 35 + 12n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (7 + n)(5 + n) = 0Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7Subproblem 2
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 = -5Solution
n = {-7, -5}
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