3(a+12)a=18

Solution for 3(a+12)a=18 equation:

Simplifying
3(a + 12) * a = 18

Reorder the terms:
3(12 + a) * a = 18

Reorder the terms for easier multiplication:
3a(12 + a) = 18
(12 * 3a + a * 3a) = 18
(36a + 3a2) = 18

Solving
36a + 3a2 = 18

Solving for variable 'a'.

Reorder the terms:
-18 + 36a + 3a2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 36a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 12a + a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + 12a + a2)' equal to zero and attempt to solve:

Simplifying
-6 + 12a + a2 = 0

Solving
-6 + 12a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 12a + 6 + a2 = 0 + 6

Reorder the terms:
-6 + 6 + 12a + a2 = 0 + 6

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

Combine like terms: 0 + 6 = 6
12a + a2 = 6

The a term is 12a.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12a + 36 + a2 = 6 + 36

Reorder the terms:
36 + 12a + a2 = 6 + 36

Combine like terms: 6 + 36 = 42
36 + 12a + a2 = 42

Factor a perfect square on the left side:
(a + 6)(a + 6) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(a + 6) equal to 6.480740698 and -6.480740698.

Subproblem 1
a + 6 = 6.480740698

Simplifying
a + 6 = 6.480740698

Reorder the terms:
6 + a = 6.480740698

Solving
6 + a = 6.480740698

Solving for variable 'a'.

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 = 6.480740698 + -6

Combine like terms: 6 + -6 = 0
0 + a = 6.480740698 + -6
a = 6.480740698 + -6

Combine like terms: 6.480740698 + -6 = 0.480740698
a = 0.480740698

Simplifying
a = 0.480740698

Subproblem 2
a + 6 = -6.480740698

Simplifying
a + 6 = -6.480740698

Reorder the terms:
6 + a = -6.480740698

Solving
6 + a = -6.480740698

Solving for variable 'a'.

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 = -6.480740698 + -6

Combine like terms: 6 + -6 = 0
0 + a = -6.480740698 + -6
a = -6.480740698 + -6

Combine like terms: -6.480740698 + -6 = -12.480740698
a = -12.480740698

Simplifying
a = -12.480740698

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.480740698, -12.480740698}
Solution
a = {0.480740698, -12.480740698}