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

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

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

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

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

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

Combine like terms: 12a + -36a = -24a
(-12 + -24a + 36a2) = 0

Solving
-12 + -24a + 36a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-1 + -2a + 3a2) = 0

Factor a trinomial.
12((-1 + -3a)(1 + -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 '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Solution
a = {-0.3333333333, 1}