r(13r+5)=8

Solution for r(13r+5)=8 equation:

Simplifying
r(13r + 5) = 8

Reorder the terms:
r(5 + 13r) = 8
(5 * r + 13r * r) = 8
(5r + 13r2) = 8

Solving
5r + 13r2 = 8

Solving for variable 'r'.

Reorder the terms:
-8 + 5r + 13r2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 5r + 13r2 = 0

Factor a trinomial.
(-1 + -1r)(8 + -13r) = 0

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

Simplifying
-1 + -1r = 0

Solving
-1 + -1r = 0

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

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

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

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

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

Simplifying
r = -1
Subproblem 2
Set the factor '(8 + -13r)' equal to zero and attempt to solve:

Simplifying
8 + -13r = 0

Solving
8 + -13r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -13r = 0 + -8

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

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

Divide each side by '-13'.
r = 0.6153846154

Simplifying
r = 0.6153846154
Solution
r = {-1, 0.6153846154}