5q^2+13q-6=0

Solution for 5q^2+13q-6=0 equation:

Simplifying
5q2 + 13q + -6 = 0

Reorder the terms:
-6 + 13q + 5q2 = 0

Solving
-6 + 13q + 5q2 = 0

Solving for variable 'q'.

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

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

Simplifying
-3 + -1q = 0

Solving
-3 + -1q = 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 + -1q = 0 + 3

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

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

Divide each side by '-1'.
q = -3

Simplifying
q = -3
Subproblem 2
Set the factor '(2 + -5q)' equal to zero and attempt to solve:

Simplifying
2 + -5q = 0

Solving
2 + -5q = 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 + -5q = 0 + -2

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

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

Divide each side by '-5'.
q = 0.4

Simplifying
q = 0.4
Solution
q = {-3, 0.4}