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Simplifying (2n + 1)(3n + 8) = 0 Reorder the terms: (1 + 2n)(3n + 8) = 0 Reorder the terms: (1 + 2n)(8 + 3n) = 0 Multiply (1 + 2n) * (8 + 3n) (1(8 + 3n) + 2n * (8 + 3n)) = 0 ((8 * 1 + 3n * 1) + 2n * (8 + 3n)) = 0 ((8 + 3n) + 2n * (8 + 3n)) = 0 (8 + 3n + (8 * 2n + 3n * 2n)) = 0 (8 + 3n + (16n + 6n2)) = 0 Combine like terms: 3n + 16n = 19n (8 + 19n + 6n2) = 0 Solving 8 + 19n + 6n2 = 0 Solving for variable 'n'. Factor a trinomial. (8 + 3n)(1 + 2n) = 0Subproblem 1
Set the factor '(8 + 3n)' equal to zero and attempt to solve: Simplifying 8 + 3n = 0 Solving 8 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3n = 0 + -8 3n = 0 + -8 Combine like terms: 0 + -8 = -8 3n = -8 Divide each side by '3'. n = -2.666666667 Simplifying n = -2.666666667Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 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 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Solution
n = {-2.666666667, -0.5}
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