(2x+2)(2x+4)=340

Solution for (2x+2)(2x+4)=340 equation:

Simplifying
(2x + 2)(2x + 4) = 340

Reorder the terms:
(2 + 2x)(2x + 4) = 340

Reorder the terms:
(2 + 2x)(4 + 2x) = 340

Multiply (2 + 2x) * (4 + 2x)
(2(4 + 2x) + 2x * (4 + 2x)) = 340
((4 * 2 + 2x * 2) + 2x * (4 + 2x)) = 340
((8 + 4x) + 2x * (4 + 2x)) = 340
(8 + 4x + (4 * 2x + 2x * 2x)) = 340
(8 + 4x + (8x + 4x2)) = 340

Combine like terms: 4x + 8x = 12x
(8 + 12x + 4x2) = 340

Solving
8 + 12x + 4x2 = 340

Solving for variable 'x'.

Reorder the terms:
8 + -340 + 12x + 4x2 = 340 + -340

Combine like terms: 8 + -340 = -332
-332 + 12x + 4x2 = 340 + -340

Combine like terms: 340 + -340 = 0
-332 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-83 + 3x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-83 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-83 + 3x + x2 = 0

Solving
-83 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '83' to each side of the equation.
-83 + 3x + 83 + x2 = 0 + 83

Reorder the terms:
-83 + 83 + 3x + x2 = 0 + 83

Combine like terms: -83 + 83 = 0
0 + 3x + x2 = 0 + 83
3x + x2 = 0 + 83

Combine like terms: 0 + 83 = 83
3x + x2 = 83

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 83 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 83 + 2.25

Combine like terms: 83 + 2.25 = 85.25
2.25 + 3x + x2 = 85.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(x + 1.5) equal to 9.233092656 and -9.233092656.

Subproblem 1
x + 1.5 = 9.233092656

Simplifying
x + 1.5 = 9.233092656

Reorder the terms:
1.5 + x = 9.233092656

Solving
1.5 + x = 9.233092656

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 9.233092656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 9.233092656 + -1.5
x = 9.233092656 + -1.5

Combine like terms: 9.233092656 + -1.5 = 7.733092656
x = 7.733092656

Simplifying
x = 7.733092656

Subproblem 2
x + 1.5 = -9.233092656

Simplifying
x + 1.5 = -9.233092656

Reorder the terms:
1.5 + x = -9.233092656

Solving
1.5 + x = -9.233092656

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -9.233092656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -9.233092656 + -1.5
x = -9.233092656 + -1.5

Combine like terms: -9.233092656 + -1.5 = -10.733092656
x = -10.733092656

Simplifying
x = -10.733092656

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.733092656, -10.733092656}
Solution
x = {7.733092656, -10.733092656}