(r-3)(r-8)=0

Solution for (r-3)(r-8)=0 equation:

Simplifying
(r + -3)(r + -8) = 0

Reorder the terms:
(-3 + r)(r + -8) = 0

Reorder the terms:
(-3 + r)(-8 + r) = 0

Multiply (-3 + r) * (-8 + r)
(-3(-8 + r) + r(-8 + r)) = 0
((-8 * -3 + r * -3) + r(-8 + r)) = 0
((24 + -3r) + r(-8 + r)) = 0
(24 + -3r + (-8 * r + r * r)) = 0
(24 + -3r + (-8r + r2)) = 0

Combine like terms: -3r + -8r = -11r
(24 + -11r + r2) = 0

Solving
24 + -11r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -1r)(8 + -1r) = 0

Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
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 = {3, 8}