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Simplifying n2 + -6n + 15 = 7 Reorder the terms: 15 + -6n + n2 = 7 Solving 15 + -6n + n2 = 7 Solving for variable 'n'. Reorder the terms: 15 + -7 + -6n + n2 = 7 + -7 Combine like terms: 15 + -7 = 8 8 + -6n + n2 = 7 + -7 Combine like terms: 7 + -7 = 0 8 + -6n + n2 = 0 Factor a trinomial. (2 + -1n)(4 + -1n) = 0Subproblem 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 '(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 = {2, 4}
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