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

Subproblem 1
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
Subproblem 2
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
Solution
q = {-2.666666667, 0.5}