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Simplifying n2 + -20n + 105 = 9 Reorder the terms: 105 + -20n + n2 = 9 Solving 105 + -20n + n2 = 9 Solving for variable 'n'. Reorder the terms: 105 + -9 + -20n + n2 = 9 + -9 Combine like terms: 105 + -9 = 96 96 + -20n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 96 + -20n + n2 = 0 Factor a trinomial. (8 + -1n)(12 + -1n) = 0Subproblem 1
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve: Simplifying 12 + -1n = 0 Solving 12 + -1n = 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 + -1n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1n = 0 + -12 -1n = 0 + -12 Combine like terms: 0 + -12 = -12 -1n = -12 Divide each side by '-1'. n = 12 Simplifying n = 12Solution
n = {8, 12}
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