(2x+82)(7x+7)=180

Solution for (2x+82)(7x+7)=180 equation:

Simplifying
(2x + 82)(7x + 7) = 180

Reorder the terms:
(82 + 2x)(7x + 7) = 180

Reorder the terms:
(82 + 2x)(7 + 7x) = 180

Multiply (82 + 2x) * (7 + 7x)
(82(7 + 7x) + 2x * (7 + 7x)) = 180
((7 * 82 + 7x * 82) + 2x * (7 + 7x)) = 180
((574 + 574x) + 2x * (7 + 7x)) = 180
(574 + 574x + (7 * 2x + 7x * 2x)) = 180
(574 + 574x + (14x + 14x2)) = 180

Combine like terms: 574x + 14x = 588x
(574 + 588x + 14x2) = 180

Solving
574 + 588x + 14x2 = 180

Solving for variable 'x'.

Reorder the terms:
574 + -180 + 588x + 14x2 = 180 + -180

Combine like terms: 574 + -180 = 394
394 + 588x + 14x2 = 180 + -180

Combine like terms: 180 + -180 = 0
394 + 588x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(197 + 294x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(197 + 294x + 7x2)' equal to zero and attempt to solve:

Simplifying
197 + 294x + 7x2 = 0

Solving
197 + 294x + 7x2 = 0

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

Divide each side by '7'.
28.14285714 + 42x + x2 = 0

Move the constant term to the right:

Add '-28.14285714' to each side of the equation.
28.14285714 + 42x + -28.14285714 + x2 = 0 + -28.14285714

Reorder the terms:
28.14285714 + -28.14285714 + 42x + x2 = 0 + -28.14285714

Combine like terms: 28.14285714 + -28.14285714 = 0.00000000
0.00000000 + 42x + x2 = 0 + -28.14285714
42x + x2 = 0 + -28.14285714

Combine like terms: 0 + -28.14285714 = -28.14285714
42x + x2 = -28.14285714

The x term is 42x.  Take half its coefficient (21).
Square it (441) and add it to both sides.

Add '441' to each side of the equation.
42x + 441 + x2 = -28.14285714 + 441

Reorder the terms:
441 + 42x + x2 = -28.14285714 + 441

Combine like terms: -28.14285714 + 441 = 412.85714286
441 + 42x + x2 = 412.85714286

Factor a perfect square on the left side:
(x + 21)(x + 21) = 412.85714286

Calculate the square root of the right side: 20.318886359

Break this problem into two subproblems by setting 
(x + 21) equal to 20.318886359 and -20.318886359.

Subproblem 1
x + 21 = 20.318886359

Simplifying
x + 21 = 20.318886359

Reorder the terms:
21 + x = 20.318886359

Solving
21 + x = 20.318886359

Solving for variable 'x'.

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

Add '-21' to each side of the equation.
21 + -21 + x = 20.318886359 + -21

Combine like terms: 21 + -21 = 0
0 + x = 20.318886359 + -21
x = 20.318886359 + -21

Combine like terms: 20.318886359 + -21 = -0.681113641
x = -0.681113641

Simplifying
x = -0.681113641

Subproblem 2
x + 21 = -20.318886359

Simplifying
x + 21 = -20.318886359

Reorder the terms:
21 + x = -20.318886359

Solving
21 + x = -20.318886359

Solving for variable 'x'.

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

Add '-21' to each side of the equation.
21 + -21 + x = -20.318886359 + -21

Combine like terms: 21 + -21 = 0
0 + x = -20.318886359 + -21
x = -20.318886359 + -21

Combine like terms: -20.318886359 + -21 = -41.318886359
x = -41.318886359

Simplifying
x = -41.318886359

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.681113641, -41.318886359}
Solution
x = {-0.681113641, -41.318886359}