(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

Remove parenthesis around (-6 + r)
-6 + r + (r + -12) = 0

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

Remove parenthesis around (-12 + r)
-6 + r + -12 + r = 0

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

Combine like terms: -6 + -12 = -18
-18 + r + r = 0

Combine like terms: r + r = 2r
-18 + 2r = 0

Solving
-18 + 2r = 0

Solving for variable 'r'.

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

Add '18' to each side of the equation.
-18 + 18 + 2r = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 2r = 0 + 18
2r = 0 + 18

Combine like terms: 0 + 18 = 18
2r = 18

Divide each side by '2'.
r = 9

Simplifying
r = 9