(12a+4)(3a-9)=0

Solution for (12a+4)(3a-9)=0 equation:

Simplifying
(12a + 4)(3a + -9) = 0

Reorder the terms:
(4 + 12a)(3a + -9) = 0

Reorder the terms:
(4 + 12a)(-9 + 3a) = 0

Multiply (4 + 12a) * (-9 + 3a)
(4(-9 + 3a) + 12a * (-9 + 3a)) = 0
((-9 * 4 + 3a * 4) + 12a * (-9 + 3a)) = 0
((-36 + 12a) + 12a * (-9 + 3a)) = 0
(-36 + 12a + (-9 * 12a + 3a * 12a)) = 0
(-36 + 12a + (-108a + 36a2)) = 0

Combine like terms: 12a + -108a = -96a
(-36 + -96a + 36a2) = 0

Solving
-36 + -96a + 36a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-3 + -8a + 3a2) = 0

Factor a trinomial.
12((-1 + -3a)(3 + -1a)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-1 + -3a)' equal to zero and attempt to solve:

Simplifying
-1 + -3a = 0

Solving
-1 + -3a = 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 + -3a = 0 + 1

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

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

Divide each side by '-3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
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 = {-0.3333333333, 3}