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Simplifying 6n2 + 96 = 60n Reorder the terms: 96 + 6n2 = 60n Solving 96 + 6n2 = 60n Solving for variable 'n'. Reorder the terms: 96 + -60n + 6n2 = 60n + -60n Combine like terms: 60n + -60n = 0 96 + -60n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(16 + -10n + n2) = 0 Factor a trinomial. 6((2 + -1n)(8 + -1n)) = 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 '(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 = 8Solution
n = {2, 8}
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