10k^2+29k+10=0

Solution for 10k^2+29k+10=0 equation:

Simplifying
10k2 + 29k + 10 = 0

Reorder the terms:
10 + 29k + 10k2 = 0

Solving
10 + 29k + 10k2 = 0

Solving for variable 'k'.

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

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

Simplifying
5 + 2k = 0

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

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

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

Divide each side by '2'.
k = -2.5

Simplifying
k = -2.5
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 = {-2.5, -0.4}