2(x+3)(4x-2)+(x+3)=55

Solution for 2(x+3)(4x-2)+(x+3)=55 equation:

Simplifying
2(x + 3)(4x + -2) + (x + 3) = 55

Reorder the terms:
2(3 + x)(4x + -2) + (x + 3) = 55

Reorder the terms:
2(3 + x)(-2 + 4x) + (x + 3) = 55

Multiply (3 + x) * (-2 + 4x)
2(3(-2 + 4x) + x(-2 + 4x)) + (x + 3) = 55
2((-2 * 3 + 4x * 3) + x(-2 + 4x)) + (x + 3) = 55
2((-6 + 12x) + x(-2 + 4x)) + (x + 3) = 55
2(-6 + 12x + (-2 * x + 4x * x)) + (x + 3) = 55
2(-6 + 12x + (-2x + 4x2)) + (x + 3) = 55

Combine like terms: 12x + -2x = 10x
2(-6 + 10x + 4x2) + (x + 3) = 55
(-6 * 2 + 10x * 2 + 4x2 * 2) + (x + 3) = 55
(-12 + 20x + 8x2) + (x + 3) = 55

Reorder the terms:
-12 + 20x + 8x2 + (3 + x) = 55

Remove parenthesis around (3 + x)
-12 + 20x + 8x2 + 3 + x = 55

Reorder the terms:
-12 + 3 + 20x + x + 8x2 = 55

Combine like terms: -12 + 3 = -9
-9 + 20x + x + 8x2 = 55

Combine like terms: 20x + x = 21x
-9 + 21x + 8x2 = 55

Solving
-9 + 21x + 8x2 = 55

Solving for variable 'x'.

Reorder the terms:
-9 + -55 + 21x + 8x2 = 55 + -55

Combine like terms: -9 + -55 = -64
-64 + 21x + 8x2 = 55 + -55

Combine like terms: 55 + -55 = 0
-64 + 21x + 8x2 = 0

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

Divide each side by '8'.
-8 + 2.625x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 2.625x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 2.625x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 2.625x + x2 = 0 + 8
2.625x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
2.625x + x2 = 8

The x term is 2.625x.  Take half its coefficient (1.3125).
Square it (1.72265625) and add it to both sides.

Add '1.72265625' to each side of the equation.
2.625x + 1.72265625 + x2 = 8 + 1.72265625

Reorder the terms:
1.72265625 + 2.625x + x2 = 8 + 1.72265625

Combine like terms: 8 + 1.72265625 = 9.72265625
1.72265625 + 2.625x + x2 = 9.72265625

Factor a perfect square on the left side:
(x + 1.3125)(x + 1.3125) = 9.72265625

Calculate the square root of the right side: 3.118117421

Break this problem into two subproblems by setting 
(x + 1.3125) equal to 3.118117421 and -3.118117421.

Subproblem 1
x + 1.3125 = 3.118117421

Simplifying
x + 1.3125 = 3.118117421

Reorder the terms:
1.3125 + x = 3.118117421

Solving
1.3125 + x = 3.118117421

Solving for variable 'x'.

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

Add '-1.3125' to each side of the equation.
1.3125 + -1.3125 + x = 3.118117421 + -1.3125

Combine like terms: 1.3125 + -1.3125 = 0.0000
0.0000 + x = 3.118117421 + -1.3125
x = 3.118117421 + -1.3125

Combine like terms: 3.118117421 + -1.3125 = 1.805617421
x = 1.805617421

Simplifying
x = 1.805617421

Subproblem 2
x + 1.3125 = -3.118117421

Simplifying
x + 1.3125 = -3.118117421

Reorder the terms:
1.3125 + x = -3.118117421

Solving
1.3125 + x = -3.118117421

Solving for variable 'x'.

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

Add '-1.3125' to each side of the equation.
1.3125 + -1.3125 + x = -3.118117421 + -1.3125

Combine like terms: 1.3125 + -1.3125 = 0.0000
0.0000 + x = -3.118117421 + -1.3125
x = -3.118117421 + -1.3125

Combine like terms: -3.118117421 + -1.3125 = -4.430617421
x = -4.430617421

Simplifying
x = -4.430617421

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.805617421, -4.430617421}