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Simplifying -3k = -12k3 + -5k2 Reorder the terms: -3k = -5k2 + -12k3 Solving -3k = -5k2 + -12k3 Solving for variable 'k'. Reorder the terms: -3k + 5k2 + 12k3 = -5k2 + 5k2 + -12k3 + 12k3 Combine like terms: -5k2 + 5k2 = 0 -3k + 5k2 + 12k3 = 0 + -12k3 + 12k3 -3k + 5k2 + 12k3 = -12k3 + 12k3 Combine like terms: -12k3 + 12k3 = 0 -3k + 5k2 + 12k3 = 0 Factor out the Greatest Common Factor (GCF), 'k'. k(-3 + 5k + 12k2) = 0 Factor a trinomial. k((-3 + -4k)(1 + -3k)) = 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 '(-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 = -0.75Subproblem 3
Set the factor '(1 + -3k)' equal to zero and attempt to solve: Simplifying 1 + -3k = 0 Solving 1 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3k = 0 + -1 -3k = 0 + -1 Combine like terms: 0 + -1 = -1 -3k = -1 Divide each side by '-3'. k = 0.3333333333 Simplifying k = 0.3333333333Solution
k = {0, -0.75, 0.3333333333}
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