(3r-12)(12r-3)=0

Solution for (3r-12)(12r-3)=0 equation:

Simplifying
(3r + -12)(12r + -3) = 0

Reorder the terms:
(-12 + 3r)(12r + -3) = 0

Reorder the terms:
(-12 + 3r)(-3 + 12r) = 0

Multiply (-12 + 3r) * (-3 + 12r)
(-12(-3 + 12r) + 3r * (-3 + 12r)) = 0
((-3 * -12 + 12r * -12) + 3r * (-3 + 12r)) = 0
((36 + -144r) + 3r * (-3 + 12r)) = 0
(36 + -144r + (-3 * 3r + 12r * 3r)) = 0
(36 + -144r + (-9r + 36r2)) = 0

Combine like terms: -144r + -9r = -153r
(36 + -153r + 36r2) = 0

Solving
36 + -153r + 36r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '9'.
9(4 + -17r + 4r2) = 0

Factor a trinomial.
9((1 + -4r)(4 + -1r)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(1 + -4r)' equal to zero and attempt to solve:

Simplifying
1 + -4r = 0

Solving
1 + -4r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4r = 0 + -1
-4r = 0 + -1

Combine like terms: 0 + -1 = -1
-4r = -1

Divide each side by '-4'.
r = 0.25

Simplifying
r = 0.25
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {0.25, 4}