6q^2+17q+5=0

Solution for 6q^2+17q+5=0 equation:

Simplifying
6q2 + 17q + 5 = 0

Reorder the terms:
5 + 17q + 6q2 = 0

Solving
5 + 17q + 6q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(5 + 2q)(1 + 3q) = 0

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

Simplifying
5 + 2q = 0

Solving
5 + 2q = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2q = 0 + -5

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

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

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

Simplifying
q = -2.5
Subproblem 2
Set the factor '(1 + 3q)' equal to zero and attempt to solve:

Simplifying
1 + 3q = 0

Solving
1 + 3q = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3q = 0 + -1
3q = 0 + -1

Combine like terms: 0 + -1 = -1
3q = -1

Divide each side by '3'.
q = -0.3333333333

Simplifying
q = -0.3333333333
Solution
q = {-2.5, -0.3333333333}