Simplifying
k^{3} + 4k^{2} + 4k = -1k^{3} + 10k
Reorder the terms:
4k + 4k^{2} + k^{3} = -1k^{3} + 10k
Reorder the terms:
4k + 4k^{2} + k^{3} = 10k + -1k^{3}
Solving
4k + 4k^{2} + k^{3} = 10k + -1k^{3}
Solving for variable 'k'.
Reorder the terms:
4k + -10k + 4k^{2} + k^{3} + k^{3} = 10k + -1k^{3} + -10k + k^{3}
Combine like terms: 4k + -10k = -6k
-6k + 4k^{2} + k^{3} + k^{3} = 10k + -1k^{3} + -10k + k^{3}
Combine like terms: k^{3} + k^{3} = 2k^{3}
-6k + 4k^{2} + 2k^{3} = 10k + -1k^{3} + -10k + k^{3}
Reorder the terms:
-6k + 4k^{2} + 2k^{3} = 10k + -10k + -1k^{3} + k^{3}
Combine like terms: 10k + -10k = 0
-6k + 4k^{2} + 2k^{3} = 0 + -1k^{3} + k^{3}
-6k + 4k^{2} + 2k^{3} = -1k^{3} + k^{3}
Combine like terms: -1k^{3} + k^{3} = 0
-6k + 4k^{2} + 2k^{3} = 0
Factor out the Greatest Common Factor (GCF), '2k'.
2k(-3 + 2k + k^{2}) = 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}