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Simplifying (n + 8)(n + -3) = 0 Reorder the terms: (8 + n)(n + -3) = 0 Reorder the terms: (8 + n)(-3 + n) = 0 Multiply (8 + n) * (-3 + n) (8(-3 + n) + n(-3 + n)) = 0 ((-3 * 8 + n * 8) + n(-3 + n)) = 0 ((-24 + 8n) + n(-3 + n)) = 0 (-24 + 8n + (-3 * n + n * n)) = 0 (-24 + 8n + (-3n + n2)) = 0 Combine like terms: 8n + -3n = 5n (-24 + 5n + n2) = 0 Solving -24 + 5n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + -1n)(3 + -1n) = 0Subproblem 1
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 = -8Subproblem 2
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 = 3Solution
n = {-8, 3}
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