8r^2=13r+6

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

Simplifying
8r2 = 13r + 6

Reorder the terms:
8r2 = 6 + 13r

Solving
8r2 = 6 + 13r

Solving for variable 'r'.

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

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

Combine like terms: 6 + -6 = 0
-6 + -13r + 8r2 = 0 + 13r + -13r
-6 + -13r + 8r2 = 13r + -13r

Combine like terms: 13r + -13r = 0
-6 + -13r + 8r2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
r = {-0.375, 2}