20=(2x+4)(x+3)

Solution for 20=(2x+4)(x+3) equation:

Simplifying
20 = (2x + 4)(x + 3)

Reorder the terms:
20 = (4 + 2x)(x + 3)

Reorder the terms:
20 = (4 + 2x)(3 + x)

Multiply (4 + 2x) * (3 + x)
20 = (4(3 + x) + 2x * (3 + x))
20 = ((3 * 4 + x * 4) + 2x * (3 + x))
20 = ((12 + 4x) + 2x * (3 + x))
20 = (12 + 4x + (3 * 2x + x * 2x))
20 = (12 + 4x + (6x + 2x2))

Combine like terms: 4x + 6x = 10x
20 = (12 + 10x + 2x2)

Solving
20 = 12 + 10x + 2x2

Solving for variable 'x'.

Combine like terms: 20 + -12 = 8
8 + -10x + -2x2 = 12 + 10x + 2x2 + -12 + -10x + -2x2

Reorder the terms:
8 + -10x + -2x2 = 12 + -12 + 10x + -10x + 2x2 + -2x2

Combine like terms: 12 + -12 = 0
8 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2
8 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
8 + -10x + -2x2 = 0 + 2x2 + -2x2
8 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + -10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -5x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
4 + -5x + -1x2 = 0

Solving
4 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5x + x2 = 0 + 4
5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
5x + x2 = 4

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 4 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + 5x + x2 = 10.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
x + 2.5 = 3.201562119

Simplifying
x + 2.5 = 3.201562119

Reorder the terms:
2.5 + x = 3.201562119

Solving
2.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.201562119 + -2.5
x = 3.201562119 + -2.5

Combine like terms: 3.201562119 + -2.5 = 0.701562119
x = 0.701562119

Simplifying
x = 0.701562119

Subproblem 2
x + 2.5 = -3.201562119

Simplifying
x + 2.5 = -3.201562119

Reorder the terms:
2.5 + x = -3.201562119

Solving
2.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.201562119 + -2.5
x = -3.201562119 + -2.5

Combine like terms: -3.201562119 + -2.5 = -5.701562119
x = -5.701562119

Simplifying
x = -5.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.701562119, -5.701562119}
Solution
x = {0.701562119, -5.701562119}