(r-5)(r-1)=

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

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

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

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

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

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

Solving
5 + -6r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -1r)(5 + -1r) = 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 '(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 = {1, 5}