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Simplifying 9n2 + 27n + 23 = 3 Reorder the terms: 23 + 27n + 9n2 = 3 Solving 23 + 27n + 9n2 = 3 Solving for variable 'n'. Reorder the terms: 23 + -3 + 27n + 9n2 = 3 + -3 Combine like terms: 23 + -3 = 20 20 + 27n + 9n2 = 3 + -3 Combine like terms: 3 + -3 = 0 20 + 27n + 9n2 = 0 Factor a trinomial. (5 + 3n)(4 + 3n) = 0Subproblem 1
Set the factor '(5 + 3n)' equal to zero and attempt to solve: Simplifying 5 + 3n = 0 Solving 5 + 3n = 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 + 3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3n = 0 + -5 3n = 0 + -5 Combine like terms: 0 + -5 = -5 3n = -5 Divide each side by '3'. n = -1.666666667 Simplifying n = -1.666666667Subproblem 2
Set the factor '(4 + 3n)' equal to zero and attempt to solve: Simplifying 4 + 3n = 0 Solving 4 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3n = 0 + -4 3n = 0 + -4 Combine like terms: 0 + -4 = -4 3n = -4 Divide each side by '3'. n = -1.333333333 Simplifying n = -1.333333333Solution
n = {-1.666666667, -1.333333333}
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