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Simplifying (n + 4)(n + -5) = 36 Reorder the terms: (4 + n)(n + -5) = 36 Reorder the terms: (4 + n)(-5 + n) = 36 Multiply (4 + n) * (-5 + n) (4(-5 + n) + n(-5 + n)) = 36 ((-5 * 4 + n * 4) + n(-5 + n)) = 36 ((-20 + 4n) + n(-5 + n)) = 36 (-20 + 4n + (-5 * n + n * n)) = 36 (-20 + 4n + (-5n + n2)) = 36 Combine like terms: 4n + -5n = -1n (-20 + -1n + n2) = 36 Solving -20 + -1n + n2 = 36 Solving for variable 'n'. Reorder the terms: -20 + -36 + -1n + n2 = 36 + -36 Combine like terms: -20 + -36 = -56 -56 + -1n + n2 = 36 + -36 Combine like terms: 36 + -36 = 0 -56 + -1n + n2 = 0 Factor a trinomial. (-7 + -1n)(8 + -1n) = 0Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7Subproblem 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 = {-7, 8}
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