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Simplifying -1k3 + 4k2 + 21k = 0 Reorder the terms: 21k + 4k2 + -1k3 = 0 Solving 21k + 4k2 + -1k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k'. k(21 + 4k + -1k2) = 0 Factor a trinomial. k((7 + -1k)(3 + k)) = 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 '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7Subproblem 3
Set the factor '(3 + k)' equal to zero and attempt to solve: Simplifying 3 + k = 0 Solving 3 + k = 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 + k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + k = 0 + -3 k = 0 + -3 Combine like terms: 0 + -3 = -3 k = -3 Simplifying k = -3Solution
k = {0, 7, -3}
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