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Simplifying n2 = -15 + 8n Solving n2 = -15 + 8n Solving for variable 'n'. Reorder the terms: 15 + -8n + n2 = -15 + 8n + 15 + -8n Reorder the terms: 15 + -8n + n2 = -15 + 15 + 8n + -8n Combine like terms: -15 + 15 = 0 15 + -8n + n2 = 0 + 8n + -8n 15 + -8n + n2 = 8n + -8n Combine like terms: 8n + -8n = 0 15 + -8n + n2 = 0 Factor a trinomial. (3 + -1n)(5 + -1n) = 0Subproblem 1
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 = 3Subproblem 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 = {3, 5}
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