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Simplifying 3n2 = 111n + -1026 Reorder the terms: 3n2 = -1026 + 111n Solving 3n2 = -1026 + 111n Solving for variable 'n'. Reorder the terms: 1026 + -111n + 3n2 = -1026 + 111n + 1026 + -111n Reorder the terms: 1026 + -111n + 3n2 = -1026 + 1026 + 111n + -111n Combine like terms: -1026 + 1026 = 0 1026 + -111n + 3n2 = 0 + 111n + -111n 1026 + -111n + 3n2 = 111n + -111n Combine like terms: 111n + -111n = 0 1026 + -111n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(342 + -37n + n2) = 0 Factor a trinomial. 3((18 + -1n)(19 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(18 + -1n)' equal to zero and attempt to solve: Simplifying 18 + -1n = 0 Solving 18 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1n = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1n = 0 + -18 -1n = 0 + -18 Combine like terms: 0 + -18 = -18 -1n = -18 Divide each side by '-1'. n = 18 Simplifying n = 18Subproblem 2
Set the factor '(19 + -1n)' equal to zero and attempt to solve: Simplifying 19 + -1n = 0 Solving 19 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1n = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1n = 0 + -19 -1n = 0 + -19 Combine like terms: 0 + -19 = -19 -1n = -19 Divide each side by '-1'. n = 19 Simplifying n = 19Solution
n = {18, 19}
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