(2x+40)(2x+20)=396

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Solution for (2x+40)(2x+20)=396 equation: 


Simplifying
(2x + 40)(2x + 20) = 396

Reorder the terms:
(40 + 2x)(2x + 20) = 396

Reorder the terms:
(40 + 2x)(20 + 2x) = 396

Multiply (40 + 2x) * (20 + 2x)
(40(20 + 2x) + 2x * (20 + 2x)) = 396
((20 * 40 + 2x * 40) + 2x * (20 + 2x)) = 396
((800 + 80x) + 2x * (20 + 2x)) = 396
(800 + 80x + (20 * 2x + 2x * 2x)) = 396
(800 + 80x + (40x + 4x2)) = 396

Combine like terms: 80x + 40x = 120x
(800 + 120x + 4x2) = 396

Solving
800 + 120x + 4x2 = 396

Solving for variable 'x'.

Reorder the terms:
800 + -396 + 120x + 4x2 = 396 + -396

Combine like terms: 800 + -396 = 404
404 + 120x + 4x2 = 396 + -396

Combine like terms: 396 + -396 = 0
404 + 120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(101 + 30x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(101 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
101 + 30x + x2 = 0

Solving
101 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-101' to each side of the equation.
101 + 30x + -101 + x2 = 0 + -101

Reorder the terms:
101 + -101 + 30x + x2 = 0 + -101

Combine like terms: 101 + -101 = 0
0 + 30x + x2 = 0 + -101
30x + x2 = 0 + -101

Combine like terms: 0 + -101 = -101
30x + x2 = -101

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -101 + 225

Reorder the terms:
225 + 30x + x2 = -101 + 225

Combine like terms: -101 + 225 = 124
225 + 30x + x2 = 124

Factor a perfect square on the left side:
(x + 15)(x + 15) = 124

Calculate the square root of the right side: 11.135528726

Break this problem into two subproblems by setting 
(x + 15) equal to 11.135528726 and -11.135528726.


Subproblem 1
x + 15 = 11.135528726

Simplifying
x + 15 = 11.135528726

Reorder the terms:
15 + x = 11.135528726

Solving
15 + x = 11.135528726

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 11.135528726 + -15

Combine like terms: 15 + -15 = 0
0 + x = 11.135528726 + -15
x = 11.135528726 + -15

Combine like terms: 11.135528726 + -15 = -3.864471274
x = -3.864471274

Simplifying
x = -3.864471274


Subproblem 2
x + 15 = -11.135528726

Simplifying
x + 15 = -11.135528726

Reorder the terms:
15 + x = -11.135528726

Solving
15 + x = -11.135528726

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -11.135528726 + -15

Combine like terms: 15 + -15 = 0
0 + x = -11.135528726 + -15
x = -11.135528726 + -15

Combine like terms: -11.135528726 + -15 = -26.135528726
x = -26.135528726

Simplifying
x = -26.135528726


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.864471274, -26.135528726}
Solution
x = {-3.864471274, -26.135528726}

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