-8r^2+13r+6=0

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

Simplifying
-8r2 + 13r + 6 = 0

Reorder the terms:
6 + 13r + -8r2 = 0

Solving
6 + 13r + -8r2 = 0

Solving for variable 'r'.

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

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

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

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

Divide each side by '-1'.
r = 2

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

Simplifying
3 + 8r = 0

Solving
3 + 8r = 0

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

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

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

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

Divide each side by '8'.
r = -0.375

Simplifying
r = -0.375
Solution
r = {2, -0.375}