(2x+20)(2x+10)=104

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Solution for (2x+20)(2x+10)=104 equation: 


Simplifying
(2x + 20)(2x + 10) = 104

Reorder the terms:
(20 + 2x)(2x + 10) = 104

Reorder the terms:
(20 + 2x)(10 + 2x) = 104

Multiply (20 + 2x) * (10 + 2x)
(20(10 + 2x) + 2x * (10 + 2x)) = 104
((10 * 20 + 2x * 20) + 2x * (10 + 2x)) = 104
((200 + 40x) + 2x * (10 + 2x)) = 104
(200 + 40x + (10 * 2x + 2x * 2x)) = 104
(200 + 40x + (20x + 4x2)) = 104

Combine like terms: 40x + 20x = 60x
(200 + 60x + 4x2) = 104

Solving
200 + 60x + 4x2 = 104

Solving for variable 'x'.

Reorder the terms:
200 + -104 + 60x + 4x2 = 104 + -104

Combine like terms: 200 + -104 = 96
96 + 60x + 4x2 = 104 + -104

Combine like terms: 104 + -104 = 0
96 + 60x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + 15x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(24 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
24 + 15x + x2 = 0

Solving
24 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 15x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + 15x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 15x + x2 = 0 + -24
15x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
15x + x2 = -24

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -24 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -24 + 56.25

Combine like terms: -24 + 56.25 = 32.25
56.25 + 15x + x2 = 32.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 7.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
x + 7.5 = 5.678908346

Simplifying
x + 7.5 = 5.678908346

Reorder the terms:
7.5 + x = 5.678908346

Solving
7.5 + x = 5.678908346

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 5.678908346 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 5.678908346 + -7.5
x = 5.678908346 + -7.5

Combine like terms: 5.678908346 + -7.5 = -1.821091654
x = -1.821091654

Simplifying
x = -1.821091654


Subproblem 2
x + 7.5 = -5.678908346

Simplifying
x + 7.5 = -5.678908346

Reorder the terms:
7.5 + x = -5.678908346

Solving
7.5 + x = -5.678908346

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -5.678908346 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -5.678908346 + -7.5
x = -5.678908346 + -7.5

Combine like terms: -5.678908346 + -7.5 = -13.178908346
x = -13.178908346

Simplifying
x = -13.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.821091654, -13.178908346}
Solution
x = {-1.821091654, -13.178908346}

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