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Simplifying 3n(n + 1)(2n + 5) = 0 Reorder the terms: 3n(1 + n)(2n + 5) = 0 Reorder the terms: 3n(1 + n)(5 + 2n) = 0 Multiply (1 + n) * (5 + 2n) 3n(1(5 + 2n) + n(5 + 2n)) = 0 3n((5 * 1 + 2n * 1) + n(5 + 2n)) = 0 3n((5 + 2n) + n(5 + 2n)) = 0 3n(5 + 2n + (5 * n + 2n * n)) = 0 3n(5 + 2n + (5n + 2n2)) = 0 Combine like terms: 2n + 5n = 7n 3n(5 + 7n + 2n2) = 0 (5 * 3n + 7n * 3n + 2n2 * 3n) = 0 (15n + 21n2 + 6n3) = 0 Solving 15n + 21n2 + 6n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n'. 3n(5 + 7n + 2n2) = 0 Factor a trinomial. 3n((5 + 2n)(1 + n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 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 = -2.5Subproblem 3
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Solution
n = {0, -2.5, -1}
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