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.
(2 + -3q)(3 + -2q) = 0

Subproblem 1
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
Subproblem 2
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
Solution
q = {0.6666666667, 1.5}