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Simplifying 4n(n2 + 5n + 6) = 0 Reorder the terms: 4n(6 + 5n + n2) = 0 (6 * 4n + 5n * 4n + n2 * 4n) = 0 (24n + 20n2 + 4n3) = 0 Solving 24n + 20n2 + 4n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4n'. 4n(6 + 5n + n2) = 0 Factor a trinomial. 4n((3 + n)(2 + n)) = 0 Ignore the factor 4.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 '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 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 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Subproblem 3
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Solution
n = {0, -3, -2}
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