6(2a+2)6(2a+2)+3(a+4)+13a=

Solution for 6(2a+2)6(2a+2)+3(a+4)+13a= equation:

Simplifying
6(2a + 2) * 6(2a + 2) + 3(a + 4) + 13a = 0

Reorder the terms:
6(2 + 2a) * 6(2a + 2) + 3(a + 4) + 13a = 0

Reorder the terms:
6(2 + 2a) * 6(2 + 2a) + 3(a + 4) + 13a = 0

Reorder the terms for easier multiplication:
6 * 6(2 + 2a)(2 + 2a) + 3(a + 4) + 13a = 0

Multiply 6 * 6
36(2 + 2a)(2 + 2a) + 3(a + 4) + 13a = 0

Multiply (2 + 2a) * (2 + 2a)
36(2(2 + 2a) + 2a * (2 + 2a)) + 3(a + 4) + 13a = 0
36((2 * 2 + 2a * 2) + 2a * (2 + 2a)) + 3(a + 4) + 13a = 0
36((4 + 4a) + 2a * (2 + 2a)) + 3(a + 4) + 13a = 0
36(4 + 4a + (2 * 2a + 2a * 2a)) + 3(a + 4) + 13a = 0
36(4 + 4a + (4a + 4a2)) + 3(a + 4) + 13a = 0

Combine like terms: 4a + 4a = 8a
36(4 + 8a + 4a2) + 3(a + 4) + 13a = 0
(4 * 36 + 8a * 36 + 4a2 * 36) + 3(a + 4) + 13a = 0
(144 + 288a + 144a2) + 3(a + 4) + 13a = 0

Reorder the terms:
144 + 288a + 144a2 + 3(4 + a) + 13a = 0
144 + 288a + 144a2 + (4 * 3 + a * 3) + 13a = 0
144 + 288a + 144a2 + (12 + 3a) + 13a = 0

Reorder the terms:
144 + 12 + 288a + 3a + 13a + 144a2 = 0

Combine like terms: 144 + 12 = 156
156 + 288a + 3a + 13a + 144a2 = 0

Combine like terms: 288a + 3a = 291a
156 + 291a + 13a + 144a2 = 0

Combine like terms: 291a + 13a = 304a
156 + 304a + 144a2 = 0

Solving
156 + 304a + 144a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(39 + 76a + 36a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(39 + 76a + 36a2)' equal to zero and attempt to solve:

Simplifying
39 + 76a + 36a2 = 0

Solving
39 + 76a + 36a2 = 0

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

Divide each side by '36'.
1.083333333 + 2.111111111a + a2 = 0

Move the constant term to the right:

Add '-1.083333333' to each side of the equation.
1.083333333 + 2.111111111a + -1.083333333 + a2 = 0 + -1.083333333

Reorder the terms:
1.083333333 + -1.083333333 + 2.111111111a + a2 = 0 + -1.083333333

Combine like terms: 1.083333333 + -1.083333333 = 0.000000000
0.000000000 + 2.111111111a + a2 = 0 + -1.083333333
2.111111111a + a2 = 0 + -1.083333333

Combine like terms: 0 + -1.083333333 = -1.083333333
2.111111111a + a2 = -1.083333333

The a term is 2.111111111a.  Take half its coefficient (1.055555556).
Square it (1.114197532) and add it to both sides.

Add '1.114197532' to each side of the equation.
2.111111111a + 1.114197532 + a2 = -1.083333333 + 1.114197532

Reorder the terms:
1.114197532 + 2.111111111a + a2 = -1.083333333 + 1.114197532

Combine like terms: -1.083333333 + 1.114197532 = 0.030864199
1.114197532 + 2.111111111a + a2 = 0.030864199

Factor a perfect square on the left side:
(a + 1.055555556)(a + 1.055555556) = 0.030864199

Calculate the square root of the right side: 0.175682096

Break this problem into two subproblems by setting 
(a + 1.055555556) equal to 0.175682096 and -0.175682096.

Subproblem 1
a + 1.055555556 = 0.175682096

Simplifying
a + 1.055555556 = 0.175682096

Reorder the terms:
1.055555556 + a = 0.175682096

Solving
1.055555556 + a = 0.175682096

Solving for variable 'a'.

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

Add '-1.055555556' to each side of the equation.
1.055555556 + -1.055555556 + a = 0.175682096 + -1.055555556

Combine like terms: 1.055555556 + -1.055555556 = 0.000000000
0.000000000 + a = 0.175682096 + -1.055555556
a = 0.175682096 + -1.055555556

Combine like terms: 0.175682096 + -1.055555556 = -0.87987346
a = -0.87987346

Simplifying
a = -0.87987346

Subproblem 2
a + 1.055555556 = -0.175682096

Simplifying
a + 1.055555556 = -0.175682096

Reorder the terms:
1.055555556 + a = -0.175682096

Solving
1.055555556 + a = -0.175682096

Solving for variable 'a'.

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

Add '-1.055555556' to each side of the equation.
1.055555556 + -1.055555556 + a = -0.175682096 + -1.055555556

Combine like terms: 1.055555556 + -1.055555556 = 0.000000000
0.000000000 + a = -0.175682096 + -1.055555556
a = -0.175682096 + -1.055555556

Combine like terms: -0.175682096 + -1.055555556 = -1.231237652
a = -1.231237652

Simplifying
a = -1.231237652

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.87987346, -1.231237652}
Solution
a = {-0.87987346, -1.231237652}