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Simplifying 12k3 + -1k2 + -6k = 0 Reorder the terms: -6k + -1k2 + 12k3 = 0 Solving -6k + -1k2 + 12k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k'. k(-6 + -1k + 12k2) = 0 Factor a trinomial. k((-2 + -3k)(3 + -4k)) = 0Subproblem 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 '(-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 = -0.6666666667Subproblem 3
Set the factor '(3 + -4k)' equal to zero and attempt to solve: Simplifying 3 + -4k = 0 Solving 3 + -4k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4k = 0 + -3 -4k = 0 + -3 Combine like terms: 0 + -3 = -3 -4k = -3 Divide each side by '-4'. k = 0.75 Simplifying k = 0.75Solution
k = {0, -0.6666666667, 0.75}
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