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

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

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

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

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

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

Combine like terms: -5r + -1r = -6r
(1 + -6r + 5r2) = 0

Solving
1 + -6r + 5r2 = 0

Solving for variable 'r'.

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

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

Simplifying
1 + -5r = 0

Solving
1 + -5r = 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 + -5r = 0 + -1

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

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

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Subproblem 2
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
Solution
r = {0.2, 1}