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Simplifying n2 + -29n + 204 = 0 Reorder the terms: 204 + -29n + n2 = 0 Solving 204 + -29n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (12 + -1n)(17 + -1n) = 0Subproblem 1
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 = 12Subproblem 2
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 = 17Solution
n = {12, 17}
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