6q^2+13q+6=0

Solution for 6q^2+13q+6=0 equation:

Simplifying
6q2 + 13q + 6 = 0

Reorder the terms:
6 + 13q + 6q2 = 0

Solving
6 + 13q + 6q2 = 0

Solving for variable 'q'.

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

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

Simplifying
3 + 2q = 0

Solving
3 + 2q = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2q = 0 + -3

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

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

Divide each side by '2'.
q = -1.5

Simplifying
q = -1.5
Subproblem 2
Set the factor '(2 + 3q)' equal to zero and attempt to solve:

Simplifying
2 + 3q = 0

Solving
2 + 3q = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3q = 0 + -2

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

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

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

Simplifying
q = -0.6666666667
Solution
q = {-1.5, -0.6666666667}