(r-6)(r-3)=0

Solution for (r-6)(r-3)=0 equation:

Simplifying
(r + -6)(r + -3) = 0

Reorder the terms:
(-6 + r)(r + -3) = 0

Reorder the terms:
(-6 + r)(-3 + r) = 0

Multiply (-6 + r) * (-3 + r)
(-6(-3 + r) + r(-3 + r)) = 0
((-3 * -6 + r * -6) + r(-3 + r)) = 0
((18 + -6r) + r(-3 + r)) = 0
(18 + -6r + (-3 * r + r * r)) = 0
(18 + -6r + (-3r + r2)) = 0

Combine like terms: -6r + -3r = -9r
(18 + -9r + r2) = 0

Solving
18 + -9r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -1r)(6 + -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 '(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 = {3, 6}