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Simplifying 3n2 + 10n + 16 = 8 Reorder the terms: 16 + 10n + 3n2 = 8 Solving 16 + 10n + 3n2 = 8 Solving for variable 'n'. Reorder the terms: 16 + -8 + 10n + 3n2 = 8 + -8 Combine like terms: 16 + -8 = 8 8 + 10n + 3n2 = 8 + -8 Combine like terms: 8 + -8 = 0 8 + 10n + 3n2 = 0 Factor a trinomial. (2 + n)(4 + 3n) = 0Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 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 = {-2, -1.333333333}
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