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Simplifying 18n2 + 6n = 60 Reorder the terms: 6n + 18n2 = 60 Solving 6n + 18n2 = 60 Solving for variable 'n'. Reorder the terms: -60 + 6n + 18n2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 6n + 18n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-10 + n + 3n2) = 0 Factor a trinomial. 6((-2 + -1n)(5 + -3n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 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 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. 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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