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Simplifying
k3 + 4k2 + 4k = -1k3 + 10k

Reorder the terms:
4k + 4k2 + k3 = -1k3 + 10k

Reorder the terms:
4k + 4k2 + k3 = 10k + -1k3

Solving
4k + 4k2 + k3 = 10k + -1k3

Solving for variable 'k'.

Reorder the terms:
4k + -10k + 4k2 + k3 + k3 = 10k + -1k3 + -10k + k3

Combine like terms: 4k + -10k = -6k
-6k + 4k2 + k3 + k3 = 10k + -1k3 + -10k + k3

Combine like terms: k3 + k3 = 2k3
-6k + 4k2 + 2k3 = 10k + -1k3 + -10k + k3

Reorder the terms:
-6k + 4k2 + 2k3 = 10k + -10k + -1k3 + k3

Combine like terms: 10k + -10k = 0
-6k + 4k2 + 2k3 = 0 + -1k3 + k3
-6k + 4k2 + 2k3 = -1k3 + k3

Combine like terms: -1k3 + k3 = 0
-6k + 4k2 + 2k3 = 0

Factor out the Greatest Common Factor (GCF), '2k'.
2k(-3 + 2k + k2) = 0

Factor a trinomial.
2k((-3 + -1k)(1 + -1k)) = 0

Ignore the factor 2.

Subproblem 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 = 0

Subproblem 2

Set the factor '(-3 + -1k)' equal to zero and attempt to solve: Simplifying -3 + -1k = 0 Solving -3 + -1k = 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 + -1k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1k = 0 + 3 -1k = 0 + 3 Combine like terms: 0 + 3 = 3 -1k = 3 Divide each side by '-1'. k = -3 Simplifying k = -3

Subproblem 3

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 = 1

Solution

k = {0, -3, 1}
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