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Simplifying 8n2 = 56n + -80 Reorder the terms: 8n2 = -80 + 56n Solving 8n2 = -80 + 56n Solving for variable 'n'. Reorder the terms: 80 + -56n + 8n2 = -80 + 56n + 80 + -56n Reorder the terms: 80 + -56n + 8n2 = -80 + 80 + 56n + -56n Combine like terms: -80 + 80 = 0 80 + -56n + 8n2 = 0 + 56n + -56n 80 + -56n + 8n2 = 56n + -56n Combine like terms: 56n + -56n = 0 80 + -56n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(10 + -7n + n2) = 0 Factor a trinomial. 8((2 + -1n)(5 + -1n)) = 0 Ignore the factor 8.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 '(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, 5}
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