6q^2-13q-8=0

Solution for 6q^2-13q-8=0 equation:

Simplifying
6q2 + -13q + -8 = 0

Reorder the terms:
-8 + -13q + 6q2 = 0

Solving
-8 + -13q + 6q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-1 + -2q)(8 + -3q) = 0

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

Simplifying
-1 + -2q = 0

Solving
-1 + -2q = 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 + -2q = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2q = 0 + 1
-2q = 0 + 1

Combine like terms: 0 + 1 = 1
-2q = 1

Divide each side by '-2'.
q = -0.5

Simplifying
q = -0.5
Subproblem 2
Set the factor '(8 + -3q)' equal to zero and attempt to solve:

Simplifying
8 + -3q = 0

Solving
8 + -3q = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3q = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3q = 0 + -8
-3q = 0 + -8

Combine like terms: 0 + -8 = -8
-3q = -8

Divide each side by '-3'.
q = 2.666666667

Simplifying
q = 2.666666667
Solution
q = {-0.5, 2.666666667}