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Simplifying n2 + -19n + 66 = 6 Reorder the terms: 66 + -19n + n2 = 6 Solving 66 + -19n + n2 = 6 Solving for variable 'n'. Reorder the terms: 66 + -6 + -19n + n2 = 6 + -6 Combine like terms: 66 + -6 = 60 60 + -19n + n2 = 6 + -6 Combine like terms: 6 + -6 = 0 60 + -19n + n2 = 0 Factor a trinomial. (4 + -1n)(15 + -1n) = 0Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve: Simplifying 15 + -1n = 0 Solving 15 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1n = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1n = 0 + -15 -1n = 0 + -15 Combine like terms: 0 + -15 = -15 -1n = -15 Divide each side by '-1'. n = 15 Simplifying n = 15Solution
n = {4, 15}
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