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Simplifying (2n + 5)(3n + 8) = 0 Reorder the terms: (5 + 2n)(3n + 8) = 0 Reorder the terms: (5 + 2n)(8 + 3n) = 0 Multiply (5 + 2n) * (8 + 3n) (5(8 + 3n) + 2n * (8 + 3n)) = 0 ((8 * 5 + 3n * 5) + 2n * (8 + 3n)) = 0 ((40 + 15n) + 2n * (8 + 3n)) = 0 (40 + 15n + (8 * 2n + 3n * 2n)) = 0 (40 + 15n + (16n + 6n2)) = 0 Combine like terms: 15n + 16n = 31n (40 + 31n + 6n2) = 0 Solving 40 + 31n + 6n2 = 0 Solving for variable 'n'. Factor a trinomial. (8 + 3n)(5 + 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 '(5 + 2n)' equal to zero and attempt to solve: Simplifying 5 + 2n = 0 Solving 5 + 2n = 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 + 2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2n = 0 + -5 2n = 0 + -5 Combine like terms: 0 + -5 = -5 2n = -5 Divide each side by '2'. n = -2.5 Simplifying n = -2.5Solution
n = {-2.666666667, -2.5}
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