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Simplifying (n + -6)(n + -6) = 9 Reorder the terms: (-6 + n)(n + -6) = 9 Reorder the terms: (-6 + n)(-6 + n) = 9 Multiply (-6 + n) * (-6 + n) (-6(-6 + n) + n(-6 + n)) = 9 ((-6 * -6 + n * -6) + n(-6 + n)) = 9 ((36 + -6n) + n(-6 + n)) = 9 (36 + -6n + (-6 * n + n * n)) = 9 (36 + -6n + (-6n + n2)) = 9 Combine like terms: -6n + -6n = -12n (36 + -12n + n2) = 9 Solving 36 + -12n + n2 = 9 Solving for variable 'n'. Reorder the terms: 36 + -9 + -12n + n2 = 9 + -9 Combine like terms: 36 + -9 = 27 27 + -12n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 27 + -12n + n2 = 0 Factor a trinomial. (3 + -1n)(9 + -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 '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Solution
n = {3, 9}
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