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}