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Simplifying 9n2 + 30n = -24 Reorder the terms: 30n + 9n2 = -24 Solving 30n + 9n2 = -24 Solving for variable 'n'. Reorder the terms: 24 + 30n + 9n2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 30n + 9n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 10n + 3n2) = 0 Factor a trinomial. 3((2 + n)(4 + 3n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 2
Set the factor '(4 + 3n)' equal to zero and attempt to solve: Simplifying 4 + 3n = 0 Solving 4 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3n = 0 + -4 3n = 0 + -4 Combine like terms: 0 + -4 = -4 3n = -4 Divide each side by '3'. n = -1.333333333 Simplifying n = -1.333333333Solution
n = {-2, -1.333333333}
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