2(a+6)(a+6)=46

Solution for 2(a+6)(a+6)=46 equation:

Simplifying
2(a + 6)(a + 6) = 46

Reorder the terms:
2(6 + a)(a + 6) = 46

Reorder the terms:
2(6 + a)(6 + a) = 46

Multiply (6 + a) * (6 + a)
2(6(6 + a) + a(6 + a)) = 46
2((6 * 6 + a * 6) + a(6 + a)) = 46
2((36 + 6a) + a(6 + a)) = 46
2(36 + 6a + (6 * a + a * a)) = 46
2(36 + 6a + (6a + a2)) = 46

Combine like terms: 6a + 6a = 12a
2(36 + 12a + a2) = 46
(36 * 2 + 12a * 2 + a2 * 2) = 46
(72 + 24a + 2a2) = 46

Solving
72 + 24a + 2a2 = 46

Solving for variable 'a'.

Reorder the terms:
72 + -46 + 24a + 2a2 = 46 + -46

Combine like terms: 72 + -46 = 26
26 + 24a + 2a2 = 46 + -46

Combine like terms: 46 + -46 = 0
26 + 24a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 12a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(13 + 12a + a2)' equal to zero and attempt to solve:

Simplifying
13 + 12a + a2 = 0

Solving
13 + 12a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 12a + -13 + a2 = 0 + -13

Reorder the terms:
13 + -13 + 12a + a2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 12a + a2 = 0 + -13
12a + a2 = 0 + -13

Combine like terms: 0 + -13 = -13
12a + a2 = -13

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 = -13 + 36

Reorder the terms:
36 + 12a + a2 = -13 + 36

Combine like terms: -13 + 36 = 23
36 + 12a + a2 = 23

Factor a perfect square on the left side:
(a + 6)(a + 6) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(a + 6) equal to 4.795831523 and -4.795831523.

Subproblem 1
a + 6 = 4.795831523

Simplifying
a + 6 = 4.795831523

Reorder the terms:
6 + a = 4.795831523

Solving
6 + a = 4.795831523

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 = 4.795831523 + -6

Combine like terms: 6 + -6 = 0
0 + a = 4.795831523 + -6
a = 4.795831523 + -6

Combine like terms: 4.795831523 + -6 = -1.204168477
a = -1.204168477

Simplifying
a = -1.204168477

Subproblem 2
a + 6 = -4.795831523

Simplifying
a + 6 = -4.795831523

Reorder the terms:
6 + a = -4.795831523

Solving
6 + a = -4.795831523

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 = -4.795831523 + -6

Combine like terms: 6 + -6 = 0
0 + a = -4.795831523 + -6
a = -4.795831523 + -6

Combine like terms: -4.795831523 + -6 = -10.795831523
a = -10.795831523

Simplifying
a = -10.795831523

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-1.204168477, -10.795831523}
Solution
a = {-1.204168477, -10.795831523}