x+6+x+3+x+9=2(x+4)2(x+1)

Solution for x+6+x+3+x+9=2(x+4)2(x+1) equation:

Simplifying
x + 6 + x + 3 + x + 9 = 2(x + 4) * 2(x + 1)

Reorder the terms:
6 + 3 + 9 + x + x + x = 2(x + 4) * 2(x + 1)

Combine like terms: 6 + 3 = 9
9 + 9 + x + x + x = 2(x + 4) * 2(x + 1)

Combine like terms: 9 + 9 = 18
18 + x + x + x = 2(x + 4) * 2(x + 1)

Combine like terms: x + x = 2x
18 + 2x + x = 2(x + 4) * 2(x + 1)

Combine like terms: 2x + x = 3x
18 + 3x = 2(x + 4) * 2(x + 1)

Reorder the terms:
18 + 3x = 2(4 + x) * 2(x + 1)

Reorder the terms:
18 + 3x = 2(4 + x) * 2(1 + x)

Reorder the terms for easier multiplication:
18 + 3x = 2 * 2(4 + x)(1 + x)

Multiply 2 * 2
18 + 3x = 4(4 + x)(1 + x)

Multiply (4 + x) * (1 + x)
18 + 3x = 4(4(1 + x) + x(1 + x))
18 + 3x = 4((1 * 4 + x * 4) + x(1 + x))
18 + 3x = 4((4 + 4x) + x(1 + x))
18 + 3x = 4(4 + 4x + (1 * x + x * x))
18 + 3x = 4(4 + 4x + (1x + x2))

Combine like terms: 4x + 1x = 5x
18 + 3x = 4(4 + 5x + x2)
18 + 3x = (4 * 4 + 5x * 4 + x2 * 4)
18 + 3x = (16 + 20x + 4x2)

Solving
18 + 3x = 16 + 20x + 4x2

Solving for variable 'x'.

Reorder the terms:
18 + -16 + 3x + -20x + -4x2 = 16 + 20x + 4x2 + -16 + -20x + -4x2

Combine like terms: 18 + -16 = 2
2 + 3x + -20x + -4x2 = 16 + 20x + 4x2 + -16 + -20x + -4x2

Combine like terms: 3x + -20x = -17x
2 + -17x + -4x2 = 16 + 20x + 4x2 + -16 + -20x + -4x2

Reorder the terms:
2 + -17x + -4x2 = 16 + -16 + 20x + -20x + 4x2 + -4x2

Combine like terms: 16 + -16 = 0
2 + -17x + -4x2 = 0 + 20x + -20x + 4x2 + -4x2
2 + -17x + -4x2 = 20x + -20x + 4x2 + -4x2

Combine like terms: 20x + -20x = 0
2 + -17x + -4x2 = 0 + 4x2 + -4x2
2 + -17x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
2 + -17x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.5 + 4.25x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 4.25x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 4.25x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 4.25x + x2 = 0 + 0.5
4.25x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
4.25x + x2 = 0.5

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = 0.5 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = 0.5 + 4.515625

Combine like terms: 0.5 + 4.515625 = 5.015625
4.515625 + 4.25x + x2 = 5.015625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 5.015625

Calculate the square root of the right side: 2.239559108

Break this problem into two subproblems by setting 
(x + 2.125) equal to 2.239559108 and -2.239559108.

Subproblem 1
x + 2.125 = 2.239559108

Simplifying
x + 2.125 = 2.239559108

Reorder the terms:
2.125 + x = 2.239559108

Solving
2.125 + x = 2.239559108

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = 2.239559108 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = 2.239559108 + -2.125
x = 2.239559108 + -2.125

Combine like terms: 2.239559108 + -2.125 = 0.114559108
x = 0.114559108

Simplifying
x = 0.114559108

Subproblem 2
x + 2.125 = -2.239559108

Simplifying
x + 2.125 = -2.239559108

Reorder the terms:
2.125 + x = -2.239559108

Solving
2.125 + x = -2.239559108

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = -2.239559108 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = -2.239559108 + -2.125
x = -2.239559108 + -2.125

Combine like terms: -2.239559108 + -2.125 = -4.364559108
x = -4.364559108

Simplifying
x = -4.364559108

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.114559108, -4.364559108}