(r-6)(r-12)=0

Solution for (r-6)(r-12)=0 equation:

Simplifying
(r + -6)(r + -12) = 0

Reorder the terms:
(-6 + r)(r + -12) = 0

Reorder the terms:
(-6 + r)(-12 + r) = 0

Multiply (-6 + r) * (-12 + r)
(-6(-12 + r) + r(-12 + r)) = 0
((-12 * -6 + r * -6) + r(-12 + r)) = 0
((72 + -6r) + r(-12 + r)) = 0
(72 + -6r + (-12 * r + r * r)) = 0
(72 + -6r + (-12r + r2)) = 0

Combine like terms: -6r + -12r = -18r
(72 + -18r + r2) = 0

Solving
72 + -18r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + -1r)(12 + -1r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(12 + -1r)' equal to zero and attempt to solve:

Simplifying
12 + -1r = 0

Solving
12 + -1r = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1r = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1r = 0 + -12
-1r = 0 + -12

Combine like terms: 0 + -12 = -12
-1r = -12

Divide each side by '-1'.
r = 12

Simplifying
r = 12
Solution
r = {6, 12}