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Simplifying n2 + -12n + 36 = 144 Reorder the terms: 36 + -12n + n2 = 144 Solving 36 + -12n + n2 = 144 Solving for variable 'n'. Reorder the terms: 36 + -144 + -12n + n2 = 144 + -144 Combine like terms: 36 + -144 = -108 -108 + -12n + n2 = 144 + -144 Combine like terms: 144 + -144 = 0 -108 + -12n + n2 = 0 Factor a trinomial. (-6 + -1n)(18 + -1n) = 0Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 2
Set the factor '(18 + -1n)' equal to zero and attempt to solve: Simplifying 18 + -1n = 0 Solving 18 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1n = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1n = 0 + -18 -1n = 0 + -18 Combine like terms: 0 + -18 = -18 -1n = -18 Divide each side by '-1'. n = 18 Simplifying n = 18Solution
n = {-6, 18}
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