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

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

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

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

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

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

Combine like terms: 36a + 6a = 42a
(36 + 42a + 6a2) = a + 3

Reorder the terms:
36 + 42a + 6a2 = 3 + a

Solving
36 + 42a + 6a2 = 3 + a

Solving for variable 'a'.

Reorder the terms:
36 + -3 + 42a + -1a + 6a2 = 3 + a + -3 + -1a

Combine like terms: 36 + -3 = 33
33 + 42a + -1a + 6a2 = 3 + a + -3 + -1a

Combine like terms: 42a + -1a = 41a
33 + 41a + 6a2 = 3 + a + -3 + -1a

Reorder the terms:
33 + 41a + 6a2 = 3 + -3 + a + -1a

Combine like terms: 3 + -3 = 0
33 + 41a + 6a2 = 0 + a + -1a
33 + 41a + 6a2 = a + -1a

Combine like terms: a + -1a = 0
33 + 41a + 6a2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
5.5 + 6.833333333a + a2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + 6.833333333a + -5.5 + a2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + 6.833333333a + a2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + 6.833333333a + a2 = 0 + -5.5
6.833333333a + a2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
6.833333333a + a2 = -5.5

The a term is 6.833333333a.  Take half its coefficient (3.416666667).
Square it (11.67361111) and add it to both sides.

Add '11.67361111' to each side of the equation.
6.833333333a + 11.67361111 + a2 = -5.5 + 11.67361111

Reorder the terms:
11.67361111 + 6.833333333a + a2 = -5.5 + 11.67361111

Combine like terms: -5.5 + 11.67361111 = 6.17361111
11.67361111 + 6.833333333a + a2 = 6.17361111

Factor a perfect square on the left side:
(a + 3.416666667)(a + 3.416666667) = 6.17361111

Calculate the square root of the right side: 2.484675252

Break this problem into two subproblems by setting 
(a + 3.416666667) equal to 2.484675252 and -2.484675252.

Subproblem 1
a + 3.416666667 = 2.484675252

Simplifying
a + 3.416666667 = 2.484675252

Reorder the terms:
3.416666667 + a = 2.484675252

Solving
3.416666667 + a = 2.484675252

Solving for variable 'a'.

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

Add '-3.416666667' to each side of the equation.
3.416666667 + -3.416666667 + a = 2.484675252 + -3.416666667

Combine like terms: 3.416666667 + -3.416666667 = 0.000000000
0.000000000 + a = 2.484675252 + -3.416666667
a = 2.484675252 + -3.416666667

Combine like terms: 2.484675252 + -3.416666667 = -0.931991415
a = -0.931991415

Simplifying
a = -0.931991415

Subproblem 2
a + 3.416666667 = -2.484675252

Simplifying
a + 3.416666667 = -2.484675252

Reorder the terms:
3.416666667 + a = -2.484675252

Solving
3.416666667 + a = -2.484675252

Solving for variable 'a'.

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

Add '-3.416666667' to each side of the equation.
3.416666667 + -3.416666667 + a = -2.484675252 + -3.416666667

Combine like terms: 3.416666667 + -3.416666667 = 0.000000000
0.000000000 + a = -2.484675252 + -3.416666667
a = -2.484675252 + -3.416666667

Combine like terms: -2.484675252 + -3.416666667 = -5.901341919
a = -5.901341919

Simplifying
a = -5.901341919

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.931991415, -5.901341919}