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Simplifying 6n(n + 4) = 5n + -15 Reorder the terms: 6n(4 + n) = 5n + -15 (4 * 6n + n * 6n) = 5n + -15 (24n + 6n2) = 5n + -15 Reorder the terms: 24n + 6n2 = -15 + 5n Solving 24n + 6n2 = -15 + 5n Solving for variable 'n'. Reorder the terms: 15 + 24n + -5n + 6n2 = -15 + 5n + 15 + -5n Combine like terms: 24n + -5n = 19n 15 + 19n + 6n2 = -15 + 5n + 15 + -5n Reorder the terms: 15 + 19n + 6n2 = -15 + 15 + 5n + -5n Combine like terms: -15 + 15 = 0 15 + 19n + 6n2 = 0 + 5n + -5n 15 + 19n + 6n2 = 5n + -5n Combine like terms: 5n + -5n = 0 15 + 19n + 6n2 = 0 Factor a trinomial. (5 + 3n)(3 + 2n) = 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 '(3 + 2n)' equal to zero and attempt to solve: Simplifying 3 + 2n = 0 Solving 3 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2n = 0 + -3 2n = 0 + -3 Combine like terms: 0 + -3 = -3 2n = -3 Divide each side by '2'. n = -1.5 Simplifying n = -1.5Solution
n = {-1.666666667, -1.5}
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