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Simplifying 5n2 = 160 + -20n Solving 5n2 = 160 + -20n Solving for variable 'n'. Reorder the terms: -160 + 20n + 5n2 = 160 + -20n + -160 + 20n Reorder the terms: -160 + 20n + 5n2 = 160 + -160 + -20n + 20n Combine like terms: 160 + -160 = 0 -160 + 20n + 5n2 = 0 + -20n + 20n -160 + 20n + 5n2 = -20n + 20n Combine like terms: -20n + 20n = 0 -160 + 20n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-32 + 4n + n2) = 0 Factor a trinomial. 5((-8 + -1n)(4 + -1n)) = 0 Ignore the factor 5.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 '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {-8, 4}
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