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Simplifying n2 + 12n + -76 = 9 Reorder the terms: -76 + 12n + n2 = 9 Solving -76 + 12n + n2 = 9 Solving for variable 'n'. Reorder the terms: -76 + -9 + 12n + n2 = 9 + -9 Combine like terms: -76 + -9 = -85 -85 + 12n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 -85 + 12n + n2 = 0 Factor a trinomial. (-17 + -1n)(5 + -1n) = 0Subproblem 1
Set the factor '(-17 + -1n)' equal to zero and attempt to solve: Simplifying -17 + -1n = 0 Solving -17 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -1n = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1n = 0 + 17 -1n = 0 + 17 Combine like terms: 0 + 17 = 17 -1n = 17 Divide each side by '-1'. n = -17 Simplifying n = -17Subproblem 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 = {-17, 5}
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