5k^2+k=0

Solution for 5k^2+k=0 equation:

Simplifying
5k2 + k = 0

Reorder the terms:
k + 5k2 = 0

Solving
k + 5k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(1 + 5k) = 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 + 5k)' equal to zero and attempt to solve:

Simplifying
1 + 5k = 0

Solving
1 + 5k = 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 + 5k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5k = 0 + -1
5k = 0 + -1

Combine like terms: 0 + -1 = -1
5k = -1

Divide each side by '5'.
k = -0.2

Simplifying
k = -0.2
Solution
k = {0, -0.2}