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Simplifying 9n2 + -51n + -168 = 0 Reorder the terms: -168 + -51n + 9n2 = 0 Solving -168 + -51n + 9n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-56 + -17n + 3n2) = 0 Factor a trinomial. 3((-7 + -3n)(8 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -3n)' equal to zero and attempt to solve: Simplifying -7 + -3n = 0 Solving -7 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3n = 0 + 7 -3n = 0 + 7 Combine like terms: 0 + 7 = 7 -3n = 7 Divide each side by '-3'. n = -2.333333333 Simplifying n = -2.333333333Subproblem 2
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 = 8Solution
n = {-2.333333333, 8}
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