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Simplifying 3n2 + 16n + 20 = -3n Reorder the terms: 20 + 16n + 3n2 = -3n Solving 20 + 16n + 3n2 = -3n Solving for variable 'n'. Reorder the terms: 20 + 16n + 3n + 3n2 = -3n + 3n Combine like terms: 16n + 3n = 19n 20 + 19n + 3n2 = -3n + 3n Combine like terms: -3n + 3n = 0 20 + 19n + 3n2 = 0 Factor a trinomial. (5 + n)(4 + 3n) = 0Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Subproblem 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 = {-5, -1.333333333}
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