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Simplifying 16n2 + -161n = -5n2 + -280 Reorder the terms: -161n + 16n2 = -5n2 + -280 Reorder the terms: -161n + 16n2 = -280 + -5n2 Solving -161n + 16n2 = -280 + -5n2 Solving for variable 'n'. Reorder the terms: 280 + -161n + 16n2 + 5n2 = -280 + -5n2 + 280 + 5n2 Combine like terms: 16n2 + 5n2 = 21n2 280 + -161n + 21n2 = -280 + -5n2 + 280 + 5n2 Reorder the terms: 280 + -161n + 21n2 = -280 + 280 + -5n2 + 5n2 Combine like terms: -280 + 280 = 0 280 + -161n + 21n2 = 0 + -5n2 + 5n2 280 + -161n + 21n2 = -5n2 + 5n2 Combine like terms: -5n2 + 5n2 = 0 280 + -161n + 21n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(40 + -23n + 3n2) = 0 Factor a trinomial. 7((8 + -3n)(5 + -1n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(8 + -3n)' equal to zero and attempt to solve: Simplifying 8 + -3n = 0 Solving 8 + -3n = 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 + -3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3n = 0 + -8 -3n = 0 + -8 Combine like terms: 0 + -8 = -8 -3n = -8 Divide each side by '-3'. n = 2.666666667 Simplifying n = 2.666666667Subproblem 2
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 = 5Solution
n = {2.666666667, 5}
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