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Simplifying 6n(n + 4) = n + -20 Reorder the terms: 6n(4 + n) = n + -20 (4 * 6n + n * 6n) = n + -20 (24n + 6n2) = n + -20 Reorder the terms: 24n + 6n2 = -20 + n Solving 24n + 6n2 = -20 + n Solving for variable 'n'. Reorder the terms: 20 + 24n + -1n + 6n2 = -20 + n + 20 + -1n Combine like terms: 24n + -1n = 23n 20 + 23n + 6n2 = -20 + n + 20 + -1n Reorder the terms: 20 + 23n + 6n2 = -20 + 20 + n + -1n Combine like terms: -20 + 20 = 0 20 + 23n + 6n2 = 0 + n + -1n 20 + 23n + 6n2 = n + -1n Combine like terms: n + -1n = 0 20 + 23n + 6n2 = 0 Factor a trinomial. (5 + 2n)(4 + 3n) = 0Subproblem 1
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 = -2.5Subproblem 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 = {-2.5, -1.333333333}
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