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Simplifying 7n2 = -280 + 91n Solving 7n2 = -280 + 91n Solving for variable 'n'. Reorder the terms: 280 + -91n + 7n2 = -280 + 91n + 280 + -91n Reorder the terms: 280 + -91n + 7n2 = -280 + 280 + 91n + -91n Combine like terms: -280 + 280 = 0 280 + -91n + 7n2 = 0 + 91n + -91n 280 + -91n + 7n2 = 91n + -91n Combine like terms: 91n + -91n = 0 280 + -91n + 7n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(40 + -13n + n2) = 0 Factor a trinomial. 7((5 + -1n)(8 + -1n)) = 0 Ignore the factor 7.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 '(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 = {5, 8}
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