(2x+10)(2x+4)=120

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Solution for (2x+10)(2x+4)=120 equation: 


Simplifying
(2x + 10)(2x + 4) = 120

Reorder the terms:
(10 + 2x)(2x + 4) = 120

Reorder the terms:
(10 + 2x)(4 + 2x) = 120

Multiply (10 + 2x) * (4 + 2x)
(10(4 + 2x) + 2x * (4 + 2x)) = 120
((4 * 10 + 2x * 10) + 2x * (4 + 2x)) = 120
((40 + 20x) + 2x * (4 + 2x)) = 120
(40 + 20x + (4 * 2x + 2x * 2x)) = 120
(40 + 20x + (8x + 4x2)) = 120

Combine like terms: 20x + 8x = 28x
(40 + 28x + 4x2) = 120

Solving
40 + 28x + 4x2 = 120

Solving for variable 'x'.

Reorder the terms:
40 + -120 + 28x + 4x2 = 120 + -120

Combine like terms: 40 + -120 = -80
-80 + 28x + 4x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-80 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + 7x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-20 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + 7x + x2 = 0

Solving
-20 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 7x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 7x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 7x + x2 = 0 + 20
7x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
7x + x2 = 20

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 20 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 20 + 12.25

Combine like terms: 20 + 12.25 = 32.25
12.25 + 7x + x2 = 32.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
x + 3.5 = 5.678908346

Simplifying
x + 3.5 = 5.678908346

Reorder the terms:
3.5 + x = 5.678908346

Solving
3.5 + x = 5.678908346

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 5.678908346 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.678908346 + -3.5
x = 5.678908346 + -3.5

Combine like terms: 5.678908346 + -3.5 = 2.178908346
x = 2.178908346

Simplifying
x = 2.178908346


Subproblem 2
x + 3.5 = -5.678908346

Simplifying
x + 3.5 = -5.678908346

Reorder the terms:
3.5 + x = -5.678908346

Solving
3.5 + x = -5.678908346

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -5.678908346 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.678908346 + -3.5
x = -5.678908346 + -3.5

Combine like terms: -5.678908346 + -3.5 = -9.178908346
x = -9.178908346

Simplifying
x = -9.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.178908346, -9.178908346}
Solution
x = {2.178908346, -9.178908346}

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