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Simplifying 0 = n2 + 19n + 84 Reorder the terms: 0 = 84 + 19n + n2 Solving 0 = 84 + 19n + n2 Solving for variable 'n'. Combine like terms: 0 + -84 = -84 -84 + -19n + -1n2 = 84 + 19n + n2 + -84 + -19n + -1n2 Reorder the terms: -84 + -19n + -1n2 = 84 + -84 + 19n + -19n + n2 + -1n2 Combine like terms: 84 + -84 = 0 -84 + -19n + -1n2 = 0 + 19n + -19n + n2 + -1n2 -84 + -19n + -1n2 = 19n + -19n + n2 + -1n2 Combine like terms: 19n + -19n = 0 -84 + -19n + -1n2 = 0 + n2 + -1n2 -84 + -19n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -84 + -19n + -1n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(84 + 19n + n2) = 0 Factor a trinomial. -1((12 + n)(7 + n)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + n)' equal to zero and attempt to solve: Simplifying 12 + n = 0 Solving 12 + n = 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 + n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + n = 0 + -12 n = 0 + -12 Combine like terms: 0 + -12 = -12 n = -12 Simplifying n = -12Subproblem 2
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 = -7Solution
n = {-12, -7}
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