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Simplifying (n + -6)(n + 3) = n + 14 Reorder the terms: (-6 + n)(n + 3) = n + 14 Reorder the terms: (-6 + n)(3 + n) = n + 14 Multiply (-6 + n) * (3 + n) (-6(3 + n) + n(3 + n)) = n + 14 ((3 * -6 + n * -6) + n(3 + n)) = n + 14 ((-18 + -6n) + n(3 + n)) = n + 14 (-18 + -6n + (3 * n + n * n)) = n + 14 (-18 + -6n + (3n + n2)) = n + 14 Combine like terms: -6n + 3n = -3n (-18 + -3n + n2) = n + 14 Reorder the terms: -18 + -3n + n2 = 14 + n Solving -18 + -3n + n2 = 14 + n Solving for variable 'n'. Reorder the terms: -18 + -14 + -3n + -1n + n2 = 14 + n + -14 + -1n Combine like terms: -18 + -14 = -32 -32 + -3n + -1n + n2 = 14 + n + -14 + -1n Combine like terms: -3n + -1n = -4n -32 + -4n + n2 = 14 + n + -14 + -1n Reorder the terms: -32 + -4n + n2 = 14 + -14 + n + -1n Combine like terms: 14 + -14 = 0 -32 + -4n + n2 = 0 + n + -1n -32 + -4n + n2 = n + -1n Combine like terms: n + -1n = 0 -32 + -4n + n2 = 0 Factor a trinomial. (-4 + -1n)(8 + -1n) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {-4, 8}
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