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

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

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

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

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

Multiply (12 + 2a) * (3 + 3a)
(12(3 + 3a) + 2a * (3 + 3a)) = 0
((3 * 12 + 3a * 12) + 2a * (3 + 3a)) = 0
((36 + 36a) + 2a * (3 + 3a)) = 0
(36 + 36a + (3 * 2a + 3a * 2a)) = 0
(36 + 36a + (6a + 6a2)) = 0

Combine like terms: 36a + 6a = 42a
(36 + 42a + 6a2) = 0

Solving
36 + 42a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + 7a + a2) = 0

Factor a trinomial.
6((6 + a)(1 + a)) = 0

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

Simplifying
1 + a = 0

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

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

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

Simplifying
a = -1
Solution
a = {-6, -1}