4x+2x(3x+2x)=480

Solution for 4x+2x(3x+2x)=480 equation:

Simplifying
4x + 2x(3x + 2x) = 480

Combine like terms: 3x + 2x = 5x
4x + 2x(5x) = 480

Remove parenthesis around (5x)
4x + 2x * 5x = 480

Reorder the terms for easier multiplication:
4x + 2 * 5x * x = 480

Multiply 2 * 5
4x + 10x * x = 480

Multiply x * x
4x + 10x2 = 480

Solving
4x + 10x2 = 480

Solving for variable 'x'.

Reorder the terms:
-480 + 4x + 10x2 = 480 + -480

Combine like terms: 480 + -480 = 0
-480 + 4x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-240 + 2x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-240 + 2x + 5x2)' equal to zero and attempt to solve:

Simplifying
-240 + 2x + 5x2 = 0

Solving
-240 + 2x + 5x2 = 0

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

Divide each side by '5'.
-48 + 0.4x + x2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 0.4x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 0.4x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 0.4x + x2 = 0 + 48
0.4x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
0.4x + x2 = 48

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 48 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 48 + 0.04

Combine like terms: 48 + 0.04 = 48.04
0.04 + 0.4x + x2 = 48.04

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 48.04

Calculate the square root of the right side: 6.93108938

Break this problem into two subproblems by setting 
(x + 0.2) equal to 6.93108938 and -6.93108938.

Subproblem 1
x + 0.2 = 6.93108938

Simplifying
x + 0.2 = 6.93108938

Reorder the terms:
0.2 + x = 6.93108938

Solving
0.2 + x = 6.93108938

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 6.93108938 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 6.93108938 + -0.2
x = 6.93108938 + -0.2

Combine like terms: 6.93108938 + -0.2 = 6.73108938
x = 6.73108938

Simplifying
x = 6.73108938

Subproblem 2
x + 0.2 = -6.93108938

Simplifying
x + 0.2 = -6.93108938

Reorder the terms:
0.2 + x = -6.93108938

Solving
0.2 + x = -6.93108938

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -6.93108938 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -6.93108938 + -0.2
x = -6.93108938 + -0.2

Combine like terms: -6.93108938 + -0.2 = -7.13108938
x = -7.13108938

Simplifying
x = -7.13108938

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.73108938, -7.13108938}
Solution
x = {6.73108938, -7.13108938}