10k^2+52k+10=0

Solution for 10k^2+52k+10=0 equation:

Simplifying
10k2 + 52k + 10 = 0

Reorder the terms:
10 + 52k + 10k2 = 0

Solving
10 + 52k + 10k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 26k + 5k2) = 0

Factor a trinomial.
2((5 + k)(1 + 5k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + k)' equal to zero and attempt to solve:

Simplifying
5 + k = 0

Solving
5 + k = 0

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

Add '-5' to each side of the equation.
5 + -5 + k = 0 + -5

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

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

Simplifying
k = -5
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 = {-5, -0.2}