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Simplifying 3n2 + 24n = 60 Reorder the terms: 24n + 3n2 = 60 Solving 24n + 3n2 = 60 Solving for variable 'n'. Reorder the terms: -60 + 24n + 3n2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 24n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + 8n + n2) = 0 Factor a trinomial. 3((-10 + -1n)(2 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve: Simplifying -10 + -1n = 0 Solving -10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1n = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1n = 0 + 10 -1n = 0 + 10 Combine like terms: 0 + 10 = 10 -1n = 10 Divide each side by '-1'. n = -10 Simplifying n = -10Subproblem 2
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 = 2Solution
n = {-10, 2}
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