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