(5-1r)(6-1r)=0

Solution for (5-1r)(6-1r)=0 equation:

Simplifying
(5 + -1r)(6 + -1r) = 0

Multiply (5 + -1r) * (6 + -1r)
(5(6 + -1r) + -1r * (6 + -1r)) = 0
((6 * 5 + -1r * 5) + -1r * (6 + -1r)) = 0
((30 + -5r) + -1r * (6 + -1r)) = 0
(30 + -5r + (6 * -1r + -1r * -1r)) = 0
(30 + -5r + (-6r + 1r2)) = 0

Combine like terms: -5r + -6r = -11r
(30 + -11r + 1r2) = 0

Solving
30 + -11r + 1r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + -1r)(6 + -1r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {5, 6}