114=2(2[x+6]x)

Solution for 114=2(2[x+6]x) equation:

Simplifying
114 = 2(2[x + 6] * x)

Reorder the terms:
114 = 2(2[6 + x] * x)

Reorder the terms for easier multiplication:
114 = 2(2x[6 + x])
114 = 2([6 * 2x + x * 2x])
114 = 2([12x + 2x2])
114 = (12x * 2 + 2x2 * 2)
114 = (24x + 4x2)

Solving
114 = 24x + 4x2

Solving for variable 'x'.

Reorder the terms:
114 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2

Combine like terms: 24x + -24x = 0
114 + -24x + -4x2 = 0 + 4x2 + -4x2
114 + -24x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
114 + -24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(57 + -12x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(57 + -12x + -2x2)' equal to zero and attempt to solve:

Simplifying
57 + -12x + -2x2 = 0

Solving
57 + -12x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-28.5 + 6x + x2 = 0

Move the constant term to the right:

Add '28.5' to each side of the equation.
-28.5 + 6x + 28.5 + x2 = 0 + 28.5

Reorder the terms:
-28.5 + 28.5 + 6x + x2 = 0 + 28.5

Combine like terms: -28.5 + 28.5 = 0.0
0.0 + 6x + x2 = 0 + 28.5
6x + x2 = 0 + 28.5

Combine like terms: 0 + 28.5 = 28.5
6x + x2 = 28.5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 28.5 + 9

Reorder the terms:
9 + 6x + x2 = 28.5 + 9

Combine like terms: 28.5 + 9 = 37.5
9 + 6x + x2 = 37.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 37.5

Calculate the square root of the right side: 6.123724357

Break this problem into two subproblems by setting 
(x + 3) equal to 6.123724357 and -6.123724357.

Subproblem 1
x + 3 = 6.123724357

Simplifying
x + 3 = 6.123724357

Reorder the terms:
3 + x = 6.123724357

Solving
3 + x = 6.123724357

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 6.123724357 + -3

Combine like terms: 3 + -3 = 0
0 + x = 6.123724357 + -3
x = 6.123724357 + -3

Combine like terms: 6.123724357 + -3 = 3.123724357
x = 3.123724357

Simplifying
x = 3.123724357

Subproblem 2
x + 3 = -6.123724357

Simplifying
x + 3 = -6.123724357

Reorder the terms:
3 + x = -6.123724357

Solving
3 + x = -6.123724357

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -6.123724357 + -3

Combine like terms: 3 + -3 = 0
0 + x = -6.123724357 + -3
x = -6.123724357 + -3

Combine like terms: -6.123724357 + -3 = -9.123724357
x = -9.123724357

Simplifying
x = -9.123724357

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.123724357, -9.123724357}
Solution
x = {3.123724357, -9.123724357}