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Simplifying 9k3 + 30k2 = 24k Reorder the terms: 30k2 + 9k3 = 24k Solving 30k2 + 9k3 = 24k Solving for variable 'k'. Reorder the terms: -24k + 30k2 + 9k3 = 24k + -24k Combine like terms: 24k + -24k = 0 -24k + 30k2 + 9k3 = 0 Factor out the Greatest Common Factor (GCF), '3k'. 3k(-8 + 10k + 3k2) = 0 Factor a trinomial. 3k((-4 + -1k)(2 + -3k)) = 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 '(-4 + -1k)' equal to zero and attempt to solve: Simplifying -4 + -1k = 0 Solving -4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1k = 0 + 4 -1k = 0 + 4 Combine like terms: 0 + 4 = 4 -1k = 4 Divide each side by '-1'. k = -4 Simplifying k = -4Subproblem 3
Set the factor '(2 + -3k)' equal to zero and attempt to solve: Simplifying 2 + -3k = 0 Solving 2 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3k = 0 + -2 -3k = 0 + -2 Combine like terms: 0 + -2 = -2 -3k = -2 Divide each side by '-3'. k = 0.6666666667 Simplifying k = 0.6666666667Solution
k = {0, -4, 0.6666666667}
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