4x(2x+2)=82

Solution for 4x(2x+2)=82 equation:

Simplifying
4x(2x + 2) = 82

Reorder the terms:
4x(2 + 2x) = 82
(2 * 4x + 2x * 4x) = 82
(8x + 8x2) = 82

Solving
8x + 8x2 = 82

Solving for variable 'x'.

Reorder the terms:
-82 + 8x + 8x2 = 82 + -82

Combine like terms: 82 + -82 = 0
-82 + 8x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + 4x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-41 + 4x + 4x2)' equal to zero and attempt to solve:

Simplifying
-41 + 4x + 4x2 = 0

Solving
-41 + 4x + 4x2 = 0

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

Divide each side by '4'.
-10.25 + x + x2 = 0

Move the constant term to the right:

Add '10.25' to each side of the equation.
-10.25 + x + 10.25 + x2 = 0 + 10.25

Reorder the terms:
-10.25 + 10.25 + x + x2 = 0 + 10.25

Combine like terms: -10.25 + 10.25 = 0.00
0.00 + x + x2 = 0 + 10.25
x + x2 = 0 + 10.25

Combine like terms: 0 + 10.25 = 10.25
x + x2 = 10.25

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 10.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 10.25 + 0.25

Combine like terms: 10.25 + 0.25 = 10.5
1.25 + x2 = 10.5

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 10.5

Calculate the square root of the right side: 3.240370349

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.240370349 and -3.240370349.

Subproblem 1
x + 0.5 = 3.240370349

Simplifying
x + 0.5 = 3.240370349

Reorder the terms:
0.5 + x = 3.240370349

Solving
0.5 + x = 3.240370349

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3.240370349 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.240370349 + -0.5
x = 3.240370349 + -0.5

Combine like terms: 3.240370349 + -0.5 = 2.740370349
x = 2.740370349

Simplifying
x = 2.740370349

Subproblem 2
x + 0.5 = -3.240370349

Simplifying
x + 0.5 = -3.240370349

Reorder the terms:
0.5 + x = -3.240370349

Solving
0.5 + x = -3.240370349

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3.240370349 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.240370349 + -0.5
x = -3.240370349 + -0.5

Combine like terms: -3.240370349 + -0.5 = -3.740370349
x = -3.740370349

Simplifying
x = -3.740370349

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.740370349, -3.740370349}
Solution
x = {2.740370349, -3.740370349}