(3a-12)(12a-3)=0

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

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

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

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

Multiply (-12 + 3a) * (-3 + 12a)
(-12(-3 + 12a) + 3a * (-3 + 12a)) = 0
((-3 * -12 + 12a * -12) + 3a * (-3 + 12a)) = 0
((36 + -144a) + 3a * (-3 + 12a)) = 0
(36 + -144a + (-3 * 3a + 12a * 3a)) = 0
(36 + -144a + (-9a + 36a2)) = 0

Combine like terms: -144a + -9a = -153a
(36 + -153a + 36a2) = 0

Solving
36 + -153a + 36a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '9'.
9(4 + -17a + 4a2) = 0

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

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

Simplifying
1 + -4a = 0

Solving
1 + -4a = 0

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

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

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

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

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

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

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

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

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

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

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

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