2(x+2)2(2x+4)=43.2

Solution for 2(x+2)2(2x+4)=43.2 equation:

Simplifying
2(x + 2) * 2(2x + 4) = 43.2

Reorder the terms:
2(2 + x) * 2(2x + 4) = 43.2

Reorder the terms:
2(2 + x) * 2(4 + 2x) = 43.2

Reorder the terms for easier multiplication:
2 * 2(2 + x)(4 + 2x) = 43.2

Multiply 2 * 2
4(2 + x)(4 + 2x) = 43.2

Multiply (2 + x) * (4 + 2x)
4(2(4 + 2x) + x(4 + 2x)) = 43.2
4((4 * 2 + 2x * 2) + x(4 + 2x)) = 43.2
4((8 + 4x) + x(4 + 2x)) = 43.2
4(8 + 4x + (4 * x + 2x * x)) = 43.2
4(8 + 4x + (4x + 2x2)) = 43.2

Combine like terms: 4x + 4x = 8x
4(8 + 8x + 2x2) = 43.2
(8 * 4 + 8x * 4 + 2x2 * 4) = 43.2
(32 + 32x + 8x2) = 43.2

Solving
32 + 32x + 8x2 = 43.2

Solving for variable 'x'.

Reorder the terms:
32 + -43.2 + 32x + 8x2 = 43.2 + -43.2

Combine like terms: 32 + -43.2 = -11.2
-11.2 + 32x + 8x2 = 43.2 + -43.2

Combine like terms: 43.2 + -43.2 = 0.0
-11.2 + 32x + 8x2 = 0.0

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

Divide each side by '8'.
-1.4 + 4x + x2 = 0.0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 4x + 1.4 + x2 = 0.0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 4x + x2 = 0.0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 4x + x2 = 0.0 + 1.4
4x + x2 = 0.0 + 1.4

Combine like terms: 0.0 + 1.4 = 1.4
4x + x2 = 1.4

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 1.4 + 4

Reorder the terms:
4 + 4x + x2 = 1.4 + 4

Combine like terms: 1.4 + 4 = 5.4
4 + 4x + x2 = 5.4

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5.4

Calculate the square root of the right side: 2.323790008

Break this problem into two subproblems by setting 
(x + 2) equal to 2.323790008 and -2.323790008.

Subproblem 1
x + 2 = 2.323790008

Simplifying
x + 2 = 2.323790008

Reorder the terms:
2 + x = 2.323790008

Solving
2 + x = 2.323790008

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.323790008 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.323790008 + -2
x = 2.323790008 + -2

Combine like terms: 2.323790008 + -2 = 0.323790008
x = 0.323790008

Simplifying
x = 0.323790008

Subproblem 2
x + 2 = -2.323790008

Simplifying
x + 2 = -2.323790008

Reorder the terms:
2 + x = -2.323790008

Solving
2 + x = -2.323790008

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.323790008 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.323790008 + -2
x = -2.323790008 + -2

Combine like terms: -2.323790008 + -2 = -4.323790008
x = -4.323790008

Simplifying
x = -4.323790008

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.323790008, -4.323790008}