(r-5)(8r-1)=0

Solution for (r-5)(8r-1)=0 equation:

Simplifying
(r + -5)(8r + -1) = 0

Reorder the terms:
(-5 + r)(8r + -1) = 0

Reorder the terms:
(-5 + r)(-1 + 8r) = 0

Multiply (-5 + r) * (-1 + 8r)
(-5(-1 + 8r) + r(-1 + 8r)) = 0
((-1 * -5 + 8r * -5) + r(-1 + 8r)) = 0
((5 + -40r) + r(-1 + 8r)) = 0
(5 + -40r + (-1 * r + 8r * r)) = 0
(5 + -40r + (-1r + 8r2)) = 0

Combine like terms: -40r + -1r = -41r
(5 + -41r + 8r2) = 0

Solving
5 + -41r + 8r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -8r)(5 + -1r) = 0

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

Simplifying
1 + -8r = 0

Solving
1 + -8r = 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 + -8r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8r = 0 + -1
-8r = 0 + -1

Combine like terms: 0 + -1 = -1
-8r = -1

Divide each side by '-8'.
r = 0.125

Simplifying
r = 0.125
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {0.125, 5}