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Simplifying 3n2 + -1n = 102 Reorder the terms: -1n + 3n2 = 102 Solving -1n + 3n2 = 102 Solving for variable 'n'. Reorder the terms: -102 + -1n + 3n2 = 102 + -102 Combine like terms: 102 + -102 = 0 -102 + -1n + 3n2 = 0 Factor a trinomial. (-17 + -3n)(6 + -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 '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-5.666666667, 6}
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