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Simplifying 30n2 + -99n + 60 = 0 Reorder the terms: 60 + -99n + 30n2 = 0 Solving 60 + -99n + 30n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(20 + -33n + 10n2) = 0 Factor a trinomial. 3((4 + -5n)(5 + -2n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -5n)' equal to zero and attempt to solve: Simplifying 4 + -5n = 0 Solving 4 + -5n = 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 + -5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5n = 0 + -4 -5n = 0 + -4 Combine like terms: 0 + -4 = -4 -5n = -4 Divide each side by '-5'. n = 0.8 Simplifying n = 0.8Subproblem 2
Set the factor '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 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 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5Solution
n = {0.8, 2.5}
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