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Simplifying (n + 12)(n + -8) = 0 Reorder the terms: (12 + n)(n + -8) = 0 Reorder the terms: (12 + n)(-8 + n) = 0 Multiply (12 + n) * (-8 + n) (12(-8 + n) + n(-8 + n)) = 0 ((-8 * 12 + n * 12) + n(-8 + n)) = 0 ((-96 + 12n) + n(-8 + n)) = 0 (-96 + 12n + (-8 * n + n * n)) = 0 (-96 + 12n + (-8n + n2)) = 0 Combine like terms: 12n + -8n = 4n (-96 + 4n + n2) = 0 Solving -96 + 4n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-12 + -1n)(8 + -1n) = 0Subproblem 1
Set the factor '(-12 + -1n)' equal to zero and attempt to solve: Simplifying -12 + -1n = 0 Solving -12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1n = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1n = 0 + 12 -1n = 0 + 12 Combine like terms: 0 + 12 = 12 -1n = 12 Divide each side by '-1'. n = -12 Simplifying n = -12Subproblem 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 = {-12, 8}
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