2(2x+40)2x=680

Solution for 2(2x+40)2x=680 equation:

Simplifying
2(2x + 40) * 2x = 680

Reorder the terms:
2(40 + 2x) * 2x = 680

Reorder the terms for easier multiplication:
2 * 2x(40 + 2x) = 680

Multiply 2 * 2
4x(40 + 2x) = 680
(40 * 4x + 2x * 4x) = 680
(160x + 8x2) = 680

Solving
160x + 8x2 = 680

Solving for variable 'x'.

Reorder the terms:
-680 + 160x + 8x2 = 680 + -680

Combine like terms: 680 + -680 = 0
-680 + 160x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-85 + 20x + x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-85 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-85 + 20x + x2 = 0

Solving
-85 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 20x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + 20x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 20x + x2 = 0 + 85
20x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
20x + x2 = 85

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 85 + 100

Reorder the terms:
100 + 20x + x2 = 85 + 100

Combine like terms: 85 + 100 = 185
100 + 20x + x2 = 185

Factor a perfect square on the left side:
(x + 10)(x + 10) = 185

Calculate the square root of the right side: 13.601470509

Break this problem into two subproblems by setting 
(x + 10) equal to 13.601470509 and -13.601470509.

Subproblem 1
x + 10 = 13.601470509

Simplifying
x + 10 = 13.601470509

Reorder the terms:
10 + x = 13.601470509

Solving
10 + x = 13.601470509

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 13.601470509 + -10

Combine like terms: 10 + -10 = 0
0 + x = 13.601470509 + -10
x = 13.601470509 + -10

Combine like terms: 13.601470509 + -10 = 3.601470509
x = 3.601470509

Simplifying
x = 3.601470509

Subproblem 2
x + 10 = -13.601470509

Simplifying
x + 10 = -13.601470509

Reorder the terms:
10 + x = -13.601470509

Solving
10 + x = -13.601470509

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -13.601470509 + -10

Combine like terms: 10 + -10 = 0
0 + x = -13.601470509 + -10
x = -13.601470509 + -10

Combine like terms: -13.601470509 + -10 = -23.601470509
x = -23.601470509

Simplifying
x = -23.601470509

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.601470509, -23.601470509}
Solution
x = {3.601470509, -23.601470509}