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Simplifying 9n2 + 33n = -30 Reorder the terms: 33n + 9n2 = -30 Solving 33n + 9n2 = -30 Solving for variable 'n'. Reorder the terms: 30 + 33n + 9n2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 33n + 9n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 11n + 3n2) = 0 Factor a trinomial. 3((2 + n)(5 + 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 '(5 + 3n)' equal to zero and attempt to solve: Simplifying 5 + 3n = 0 Solving 5 + 3n = 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 + 3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3n = 0 + -5 3n = 0 + -5 Combine like terms: 0 + -5 = -5 3n = -5 Divide each side by '3'. n = -1.666666667 Simplifying n = -1.666666667Solution
n = {-2, -1.666666667}
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