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Simplifying n2 + 3n + -18 = 162 Reorder the terms: -18 + 3n + n2 = 162 Solving -18 + 3n + n2 = 162 Solving for variable 'n'. Reorder the terms: -18 + -162 + 3n + n2 = 162 + -162 Combine like terms: -18 + -162 = -180 -180 + 3n + n2 = 162 + -162 Combine like terms: 162 + -162 = 0 -180 + 3n + n2 = 0 Factor a trinomial. (-15 + -1n)(12 + -1n) = 0Subproblem 1
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 = -15Subproblem 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 = {-15, 12}
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