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Simplifying 3n2 + -360 = 21n Reorder the terms: -360 + 3n2 = 21n Solving -360 + 3n2 = 21n Solving for variable 'n'. Reorder the terms: -360 + -21n + 3n2 = 21n + -21n Combine like terms: 21n + -21n = 0 -360 + -21n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-120 + -7n + n2) = 0 Factor a trinomial. 3((-8 + -1n)(15 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve: Simplifying 15 + -1n = 0 Solving 15 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1n = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1n = 0 + -15 -1n = 0 + -15 Combine like terms: 0 + -15 = -15 -1n = -15 Divide each side by '-1'. n = 15 Simplifying n = 15Solution
n = {-8, 15}
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