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Simplifying k3 + -5k2 + 3k = -1k Reorder the terms: 3k + -5k2 + k3 = -1k Solving 3k + -5k2 + k3 = -1k Solving for variable 'k'. Reorder the terms: 3k + k + -5k2 + k3 = -1k + k Combine like terms: 3k + k = 4k 4k + -5k2 + k3 = -1k + k Combine like terms: -1k + k = 0 4k + -5k2 + k3 = 0 Factor out the Greatest Common Factor (GCF), 'k'. k(4 + -5k + k2) = 0 Factor a trinomial. k((1 + -1k)(4 + -1k)) = 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 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 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 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1Subproblem 3
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 = 4Solution
k = {0, 1, 4}
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