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Simplifying 3n2 + 2n = 85 Reorder the terms: 2n + 3n2 = 85 Solving 2n + 3n2 = 85 Solving for variable 'n'. Reorder the terms: -85 + 2n + 3n2 = 85 + -85 Combine like terms: 85 + -85 = 0 -85 + 2n + 3n2 = 0 Factor a trinomial. (-17 + -3n)(5 + -1n) = 0Subproblem 1
Set the factor '(-17 + -3n)' equal to zero and attempt to solve: Simplifying -17 + -3n = 0 Solving -17 + -3n = 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 + -3n = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -3n = 0 + 17 -3n = 0 + 17 Combine like terms: 0 + 17 = 17 -3n = 17 Divide each side by '-3'. n = -5.666666667 Simplifying n = -5.666666667Subproblem 2
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 = 5Solution
n = {-5.666666667, 5}
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