x+2x(x+2)+3x(x+2)=96

Solution for x+2x(x+2)+3x(x+2)=96 equation:

Simplifying
x + 2x(x + 2) + 3x(x + 2) = 96

Reorder the terms:
x + 2x(2 + x) + 3x(x + 2) = 96
x + (2 * 2x + x * 2x) + 3x(x + 2) = 96
x + (4x + 2x2) + 3x(x + 2) = 96

Reorder the terms:
x + 4x + 2x2 + 3x(2 + x) = 96
x + 4x + 2x2 + (2 * 3x + x * 3x) = 96
x + 4x + 2x2 + (6x + 3x2) = 96

Reorder the terms:
x + 4x + 6x + 2x2 + 3x2 = 96

Combine like terms: x + 4x = 5x
5x + 6x + 2x2 + 3x2 = 96

Combine like terms: 5x + 6x = 11x
11x + 2x2 + 3x2 = 96

Combine like terms: 2x2 + 3x2 = 5x2
11x + 5x2 = 96

Solving
11x + 5x2 = 96

Solving for variable 'x'.

Reorder the terms:
-96 + 11x + 5x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-96 + 11x + 5x2 = 0

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

Divide each side by '5'.
-19.2 + 2.2x + x2 = 0

Move the constant term to the right:

Add '19.2' to each side of the equation.
-19.2 + 2.2x + 19.2 + x2 = 0 + 19.2

Reorder the terms:
-19.2 + 19.2 + 2.2x + x2 = 0 + 19.2

Combine like terms: -19.2 + 19.2 = 0.0
0.0 + 2.2x + x2 = 0 + 19.2
2.2x + x2 = 0 + 19.2

Combine like terms: 0 + 19.2 = 19.2
2.2x + x2 = 19.2

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = 19.2 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = 19.2 + 1.21

Combine like terms: 19.2 + 1.21 = 20.41
1.21 + 2.2x + x2 = 20.41

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 20.41

Calculate the square root of the right side: 4.517742799

Break this problem into two subproblems by setting 
(x + 1.1) equal to 4.517742799 and -4.517742799.

Subproblem 1
x + 1.1 = 4.517742799

Simplifying
x + 1.1 = 4.517742799

Reorder the terms:
1.1 + x = 4.517742799

Solving
1.1 + x = 4.517742799

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = 4.517742799 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = 4.517742799 + -1.1
x = 4.517742799 + -1.1

Combine like terms: 4.517742799 + -1.1 = 3.417742799
x = 3.417742799

Simplifying
x = 3.417742799

Subproblem 2
x + 1.1 = -4.517742799

Simplifying
x + 1.1 = -4.517742799

Reorder the terms:
1.1 + x = -4.517742799

Solving
1.1 + x = -4.517742799

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = -4.517742799 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = -4.517742799 + -1.1
x = -4.517742799 + -1.1

Combine like terms: -4.517742799 + -1.1 = -5.617742799
x = -5.617742799

Simplifying
x = -5.617742799

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.417742799, -5.617742799}