6k=k^3+k^2

Solution for 6k=k^3+k^2 equation:

Simplifying
6k = k3 + k2

Reorder the terms:
6k = k2 + k3

Solving
6k = k2 + k3

Solving for variable 'k'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'k'.
k(6 + -1k + -1k2) = 0

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

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 '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Subproblem 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 = -3
Solution
k = {0, 2, -3}