4.2(x+8)+4.2x=x(x+8)

Solution for 4.2(x+8)+4.2x=x(x+8) equation:

Simplifying
4.2(x + 8) + 4.2x = x(x + 8)

Reorder the terms:
4.2(8 + x) + 4.2x = x(x + 8)
(8 * 4.2 + x * 4.2) + 4.2x = x(x + 8)
(33.6 + 4.2x) + 4.2x = x(x + 8)

Combine like terms: 4.2x + 4.2x = 8.4x
33.6 + 8.4x = x(x + 8)

Reorder the terms:
33.6 + 8.4x = x(8 + x)
33.6 + 8.4x = (8 * x + x * x)
33.6 + 8.4x = (8x + x2)

Solving
33.6 + 8.4x = 8x + x2

Solving for variable 'x'.

Combine like terms: 8.4x + -8x = 0.4x
33.6 + 0.4x + -1x2 = 8x + x2 + -8x + -1x2

Reorder the terms:
33.6 + 0.4x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
33.6 + 0.4x + -1x2 = 0 + x2 + -1x2
33.6 + 0.4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
33.6 + 0.4x + -1x2 = 0

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

Divide each side by '-1'.
-33.6 + -0.4x + x2 = 0

Move the constant term to the right:

Add '33.6' to each side of the equation.
-33.6 + -0.4x + 33.6 + x2 = 0 + 33.6

Reorder the terms:
-33.6 + 33.6 + -0.4x + x2 = 0 + 33.6

Combine like terms: -33.6 + 33.6 = 0.0
0.0 + -0.4x + x2 = 0 + 33.6
-0.4x + x2 = 0 + 33.6

Combine like terms: 0 + 33.6 = 33.6
-0.4x + x2 = 33.6

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 = 33.6 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 33.6 + 0.04

Combine like terms: 33.6 + 0.04 = 33.64
0.04 + -0.4x + x2 = 33.64

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 33.64

Calculate the square root of the right side: 5.8

Break this problem into two subproblems by setting 
(x + -0.2) equal to 5.8 and -5.8.

Subproblem 1
x + -0.2 = 5.8

Simplifying
x + -0.2 = 5.8

Reorder the terms:
-0.2 + x = 5.8

Solving
-0.2 + x = 5.8

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 = 5.8 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = 5.8 + 0.2
x = 5.8 + 0.2

Combine like terms: 5.8 + 0.2 = 6
x = 6

Simplifying
x = 6

Subproblem 2
x + -0.2 = -5.8

Simplifying
x + -0.2 = -5.8

Reorder the terms:
-0.2 + x = -5.8

Solving
-0.2 + x = -5.8

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 = -5.8 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = -5.8 + 0.2
x = -5.8 + 0.2

Combine like terms: -5.8 + 0.2 = -5.6
x = -5.6

Simplifying
x = -5.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6, -5.6}