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Simplifying n2 = 24 + -5n Solving n2 = 24 + -5n Solving for variable 'n'. Reorder the terms: -24 + 5n + n2 = 24 + -5n + -24 + 5n Reorder the terms: -24 + 5n + n2 = 24 + -24 + -5n + 5n Combine like terms: 24 + -24 = 0 -24 + 5n + n2 = 0 + -5n + 5n -24 + 5n + n2 = -5n + 5n Combine like terms: -5n + 5n = 0 -24 + 5n + n2 = 0 Factor a trinomial. (-8 + -1n)(3 + -1n) = 0Subproblem 1
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 = -8Subproblem 2
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 = 3Solution
n = {-8, 3}
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