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Simplifying 9n2 + 24n + -99 = 6 Reorder the terms: -99 + 24n + 9n2 = 6 Solving -99 + 24n + 9n2 = 6 Solving for variable 'n'. Reorder the terms: -99 + -6 + 24n + 9n2 = 6 + -6 Combine like terms: -99 + -6 = -105 -105 + 24n + 9n2 = 6 + -6 Combine like terms: 6 + -6 = 0 -105 + 24n + 9n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-35 + 8n + 3n2) = 0 Factor a trinomial. 3((-5 + -1n)(7 + -3n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5Subproblem 2
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 = 2.333333333Solution
n = {-5, 2.333333333}
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