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Simplifying 6n2 + 31n + 18 = 0 Reorder the terms: 18 + 31n + 6n2 = 0 Solving 18 + 31n + 6n2 = 0 Solving for variable 'n'. Factor a trinomial. (9 + 2n)(2 + 3n) = 0Subproblem 1
Set the factor '(9 + 2n)' equal to zero and attempt to solve: Simplifying 9 + 2n = 0 Solving 9 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2n = 0 + -9 2n = 0 + -9 Combine like terms: 0 + -9 = -9 2n = -9 Divide each side by '2'. n = -4.5 Simplifying n = -4.5Subproblem 2
Set the factor '(2 + 3n)' equal to zero and attempt to solve: Simplifying 2 + 3n = 0 Solving 2 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3n = 0 + -2 3n = 0 + -2 Combine like terms: 0 + -2 = -2 3n = -2 Divide each side by '3'. n = -0.6666666667 Simplifying n = -0.6666666667Solution
n = {-4.5, -0.6666666667}
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