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Simplifying 2k3 + 3k2 + k = 0 Reorder the terms: k + 3k2 + 2k3 = 0 Solving k + 3k2 + 2k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k'. k(1 + 3k + 2k2) = 0 Factor a trinomial. k((1 + k)(1 + 2k)) = 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 '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 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 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Subproblem 3
Set the factor '(1 + 2k)' equal to zero and attempt to solve: Simplifying 1 + 2k = 0 Solving 1 + 2k = 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 + 2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2k = 0 + -1 2k = 0 + -1 Combine like terms: 0 + -1 = -1 2k = -1 Divide each side by '2'. k = -0.5 Simplifying k = -0.5Solution
k = {0, -1, -0.5}
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