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