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Simplifying 3n2 = 5 + 14n Solving 3n2 = 5 + 14n Solving for variable 'n'. Reorder the terms: -5 + -14n + 3n2 = 5 + 14n + -5 + -14n Reorder the terms: -5 + -14n + 3n2 = 5 + -5 + 14n + -14n Combine like terms: 5 + -5 = 0 -5 + -14n + 3n2 = 0 + 14n + -14n -5 + -14n + 3n2 = 14n + -14n Combine like terms: 14n + -14n = 0 -5 + -14n + 3n2 = 0 Factor a trinomial. (-1 + -3n)(5 + -1n) = 0Subproblem 1
Set the factor '(-1 + -3n)' equal to zero and attempt to solve: Simplifying -1 + -3n = 0 Solving -1 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3n = 0 + 1 -3n = 0 + 1 Combine like terms: 0 + 1 = 1 -3n = 1 Divide each side by '-3'. n = -0.3333333333 Simplifying n = -0.3333333333Subproblem 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 = {-0.3333333333, 5}
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