r^2=12(r-3)

Solution for r^2=12(r-3) equation:

Simplifying
r2 = 12(r + -3)

Reorder the terms:
r2 = 12(-3 + r)
r2 = (-3 * 12 + r * 12)
r2 = (-36 + 12r)

Solving
r2 = -36 + 12r

Solving for variable 'r'.

Reorder the terms:
36 + -12r + r2 = -36 + 12r + 36 + -12r

Reorder the terms:
36 + -12r + r2 = -36 + 36 + 12r + -12r

Combine like terms: -36 + 36 = 0
36 + -12r + r2 = 0 + 12r + -12r
36 + -12r + r2 = 12r + -12r

Combine like terms: 12r + -12r = 0
36 + -12r + r2 = 0

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