3k^2+17k+10=0

Solution for 3k^2+17k+10=0 equation:

Simplifying
3k2 + 17k + 10 = 0

Reorder the terms:
10 + 17k + 3k2 = 0

Solving
10 + 17k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(5 + k)(2 + 3k) = 0

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 '(2 + 3k)' equal to zero and attempt to solve:

Simplifying
2 + 3k = 0

Solving
2 + 3k = 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 + 3k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3k = 0 + -2
3k = 0 + -2

Combine like terms: 0 + -2 = -2
3k = -2

Divide each side by '3'.
k = -0.6666666667

Simplifying
k = -0.6666666667
Solution
k = {-5, -0.6666666667}