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Simplifying 0 = n2 + -8n + 15 Reorder the terms: 0 = 15 + -8n + n2 Solving 0 = 15 + -8n + n2 Solving for variable 'n'. Combine like terms: 0 + -15 = -15 -15 + 8n + -1n2 = 15 + -8n + n2 + -15 + 8n + -1n2 Reorder the terms: -15 + 8n + -1n2 = 15 + -15 + -8n + 8n + n2 + -1n2 Combine like terms: 15 + -15 = 0 -15 + 8n + -1n2 = 0 + -8n + 8n + n2 + -1n2 -15 + 8n + -1n2 = -8n + 8n + n2 + -1n2 Combine like terms: -8n + 8n = 0 -15 + 8n + -1n2 = 0 + n2 + -1n2 -15 + 8n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -15 + 8n + -1n2 = 0 Factor a trinomial. (-5 + n)(3 + -1n) = 0Subproblem 1
Set the factor '(-5 + n)' equal to zero and attempt to solve: Simplifying -5 + n = 0 Solving -5 + n = 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 + n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + n = 0 + 5 n = 0 + 5 Combine like terms: 0 + 5 = 5 n = 5 Simplifying n = 5Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Solution
n = {5, 3}
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