5k^2+2k=0

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

Simplifying
5k2 + 2k = 0

Reorder the terms:
2k + 5k2 = 0

Solving
2k + 5k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(2 + 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 '(2 + 5k)' equal to zero and attempt to solve:

Simplifying
2 + 5k = 0

Solving
2 + 5k = 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 + 5k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5k = 0 + -2
5k = 0 + -2

Combine like terms: 0 + -2 = -2
5k = -2

Divide each side by '5'.
k = -0.4

Simplifying
k = -0.4
Solution
k = {0, -0.4}