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Simplifying n2 + 5n = 204 Reorder the terms: 5n + n2 = 204 Solving 5n + n2 = 204 Solving for variable 'n'. Reorder the terms: -204 + 5n + n2 = 204 + -204 Combine like terms: 204 + -204 = 0 -204 + 5n + n2 = 0 Factor a trinomial. (-17 + -1n)(12 + -1n) = 0Subproblem 1
Set the factor '(-17 + -1n)' equal to zero and attempt to solve: Simplifying -17 + -1n = 0 Solving -17 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -1n = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1n = 0 + 17 -1n = 0 + 17 Combine like terms: 0 + 17 = 17 -1n = 17 Divide each side by '-1'. n = -17 Simplifying n = -17Subproblem 2
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 = 12Solution
n = {-17, 12}
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