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Simplifying -6k3 + 21k2 + 90k = 0 Reorder the terms: 90k + 21k2 + -6k3 = 0 Solving 90k + 21k2 + -6k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3k'. 3k(30 + 7k + -2k2) = 0 Factor a trinomial. 3k((6 + -1k)(5 + 2k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve: Simplifying 6 + -1k = 0 Solving 6 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1k = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1k = 0 + -6 -1k = 0 + -6 Combine like terms: 0 + -6 = -6 -1k = -6 Divide each side by '-1'. k = 6 Simplifying k = 6Subproblem 3
Set the factor '(5 + 2k)' equal to zero and attempt to solve: Simplifying 5 + 2k = 0 Solving 5 + 2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2k = 0 + -5 2k = 0 + -5 Combine like terms: 0 + -5 = -5 2k = -5 Divide each side by '2'. k = -2.5 Simplifying k = -2.5Solution
k = {0, 6, -2.5}
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