12(a-3)-2a(a-3)=0

Solution for 12(a-3)-2a(a-3)=0 equation:

Simplifying
12(a + -3) + -2a(a + -3) = 0

Reorder the terms:
12(-3 + a) + -2a(a + -3) = 0
(-3 * 12 + a * 12) + -2a(a + -3) = 0
(-36 + 12a) + -2a(a + -3) = 0

Reorder the terms:
-36 + 12a + -2a(-3 + a) = 0
-36 + 12a + (-3 * -2a + a * -2a) = 0
-36 + 12a + (6a + -2a2) = 0

Combine like terms: 12a + 6a = 18a
-36 + 18a + -2a2 = 0

Solving
-36 + 18a + -2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 9a + -1a2) = 0

Factor a trinomial.
2((-6 + a)(3 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + a)' equal to zero and attempt to solve:

Simplifying
-6 + a = 0

Solving
-6 + a = 0

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

Add '6' to each side of the equation.
-6 + 6 + a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + a = 0 + 6
a = 0 + 6

Combine like terms: 0 + 6 = 6
a = 6

Simplifying
a = 6
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {6, 3}