3k^2+k=0

Solution for 3k^2+k=0 equation:

Simplifying
3k2 + k = 0

Reorder the terms:
k + 3k2 = 0

Solving
k + 3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(1 + 3k) = 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 '(1 + 3k)' equal to zero and attempt to solve:

Simplifying
1 + 3k = 0

Solving
1 + 3k = 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 + 3k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3k = 0 + -1
3k = 0 + -1

Combine like terms: 0 + -1 = -1
3k = -1

Divide each side by '3'.
k = -0.3333333333

Simplifying
k = -0.3333333333
Solution
k = {0, -0.3333333333}