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Simplifying n(n + 5)(2n + 9) = 0 Reorder the terms: n(5 + n)(2n + 9) = 0 Reorder the terms: n(5 + n)(9 + 2n) = 0 Multiply (5 + n) * (9 + 2n) n(5(9 + 2n) + n(9 + 2n)) = 0 n((9 * 5 + 2n * 5) + n(9 + 2n)) = 0 n((45 + 10n) + n(9 + 2n)) = 0 n(45 + 10n + (9 * n + 2n * n)) = 0 n(45 + 10n + (9n + 2n2)) = 0 Combine like terms: 10n + 9n = 19n n(45 + 19n + 2n2) = 0 (45 * n + 19n * n + 2n2 * n) = 0 (45n + 19n2 + 2n3) = 0 Solving 45n + 19n2 + 2n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(45 + 19n + 2n2) = 0 Factor a trinomial. n((5 + n)(9 + 2n)) = 0Subproblem 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 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Subproblem 3
Set the factor '(9 + 2n)' equal to zero and attempt to solve: Simplifying 9 + 2n = 0 Solving 9 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2n = 0 + -9 2n = 0 + -9 Combine like terms: 0 + -9 = -9 2n = -9 Divide each side by '2'. n = -4.5 Simplifying n = -4.5Solution
n = {0, -5, -4.5}
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