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Simplifying n2 + -10n + -75 = 0 Reorder the terms: -75 + -10n + n2 = 0 Solving -75 + -10n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -1n)(15 + -1n) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve: Simplifying 15 + -1n = 0 Solving 15 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1n = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1n = 0 + -15 -1n = 0 + -15 Combine like terms: 0 + -15 = -15 -1n = -15 Divide each side by '-1'. n = 15 Simplifying n = 15Solution
n = {-5, 15}
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