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Simplifying (n + 9)(n + -5) = 0 Reorder the terms: (9 + n)(n + -5) = 0 Reorder the terms: (9 + n)(-5 + n) = 0 Multiply (9 + n) * (-5 + n) (9(-5 + n) + n(-5 + n)) = 0 ((-5 * 9 + n * 9) + n(-5 + n)) = 0 ((-45 + 9n) + n(-5 + n)) = 0 (-45 + 9n + (-5 * n + n * n)) = 0 (-45 + 9n + (-5n + n2)) = 0 Combine like terms: 9n + -5n = 4n (-45 + 4n + n2) = 0 Solving -45 + 4n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-9 + -1n)(5 + -1n) = 0Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve: Simplifying -9 + -1n = 0 Solving -9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1n = 0 + 9 -1n = 0 + 9 Combine like terms: 0 + 9 = 9 -1n = 9 Divide each side by '-1'. n = -9 Simplifying n = -9Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-9, 5}
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