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Simplifying 3n2 = 144 + -11n Solving 3n2 = 144 + -11n Solving for variable 'n'. Reorder the terms: -144 + 11n + 3n2 = 144 + -11n + -144 + 11n Reorder the terms: -144 + 11n + 3n2 = 144 + -144 + -11n + 11n Combine like terms: 144 + -144 = 0 -144 + 11n + 3n2 = 0 + -11n + 11n -144 + 11n + 3n2 = -11n + 11n Combine like terms: -11n + 11n = 0 -144 + 11n + 3n2 = 0 Factor a trinomial. (-9 + -1n)(16 + -3n) = 0Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve: Simplifying -9 + -1n = 0 Solving -9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1n = 0 + 9 -1n = 0 + 9 Combine like terms: 0 + 9 = 9 -1n = 9 Divide each side by '-1'. n = -9 Simplifying n = -9Subproblem 2
Set the factor '(16 + -3n)' equal to zero and attempt to solve: Simplifying 16 + -3n = 0 Solving 16 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -3n = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -3n = 0 + -16 -3n = 0 + -16 Combine like terms: 0 + -16 = -16 -3n = -16 Divide each side by '-3'. n = 5.333333333 Simplifying n = 5.333333333Solution
n = {-9, 5.333333333}
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