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

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

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

Combine like terms: 3 + 2 = 5
(2 + x) * x(5) = x + 20

Reorder the terms for easier multiplication:
5x(2 + x) = x + 20
(2 * 5x + x * 5x) = x + 20
(10x + 5x2) = x + 20

Reorder the terms:
10x + 5x2 = 20 + x

Solving
10x + 5x2 = 20 + x

Solving for variable 'x'.

Reorder the terms:
-20 + 10x + -1x + 5x2 = 20 + x + -20 + -1x

Combine like terms: 10x + -1x = 9x
-20 + 9x + 5x2 = 20 + x + -20 + -1x

Reorder the terms:
-20 + 9x + 5x2 = 20 + -20 + x + -1x

Combine like terms: 20 + -20 = 0
-20 + 9x + 5x2 = 0 + x + -1x
-20 + 9x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-20 + 9x + 5x2 = 0

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

Divide each side by '5'.
-4 + 1.8x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.8x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 1.8x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.8x + x2 = 0 + 4
1.8x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
1.8x + x2 = 4

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 4 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 4 + 0.81

Combine like terms: 4 + 0.81 = 4.81
0.81 + 1.8x + x2 = 4.81

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 4.81

Calculate the square root of the right side: 2.19317122

Break this problem into two subproblems by setting 
(x + 0.9) equal to 2.19317122 and -2.19317122.

Subproblem 1
x + 0.9 = 2.19317122

Simplifying
x + 0.9 = 2.19317122

Reorder the terms:
0.9 + x = 2.19317122

Solving
0.9 + x = 2.19317122

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = 2.19317122 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 2.19317122 + -0.9
x = 2.19317122 + -0.9

Combine like terms: 2.19317122 + -0.9 = 1.29317122
x = 1.29317122

Simplifying
x = 1.29317122

Subproblem 2
x + 0.9 = -2.19317122

Simplifying
x + 0.9 = -2.19317122

Reorder the terms:
0.9 + x = -2.19317122

Solving
0.9 + x = -2.19317122

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = -2.19317122 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -2.19317122 + -0.9
x = -2.19317122 + -0.9

Combine like terms: -2.19317122 + -0.9 = -3.09317122
x = -3.09317122

Simplifying
x = -3.09317122

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.29317122, -3.09317122}