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Simplifying (n + 8)(n + -3) = -30 Reorder the terms: (8 + n)(n + -3) = -30 Reorder the terms: (8 + n)(-3 + n) = -30 Multiply (8 + n) * (-3 + n) (8(-3 + n) + n(-3 + n)) = -30 ((-3 * 8 + n * 8) + n(-3 + n)) = -30 ((-24 + 8n) + n(-3 + n)) = -30 (-24 + 8n + (-3 * n + n * n)) = -30 (-24 + 8n + (-3n + n2)) = -30 Combine like terms: 8n + -3n = 5n (-24 + 5n + n2) = -30 Solving -24 + 5n + n2 = -30 Solving for variable 'n'. Reorder the terms: -24 + 30 + 5n + n2 = -30 + 30 Combine like terms: -24 + 30 = 6 6 + 5n + n2 = -30 + 30 Combine like terms: -30 + 30 = 0 6 + 5n + n2 = 0 Factor a trinomial. (3 + n)(2 + n) = 0Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 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 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Solution
n = {-3, -2}
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