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

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

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

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

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

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

Combine like terms: -8r + -1r = -9r
(8 + -9r + r2) = 0

Solving
8 + -9r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -1r)(8 + -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 '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {1, 8}