.1x(5x+20)-5=.25(2x+8)

Solution for .1x(5x+20)-5=.25(2x+8) equation:

Simplifying
0.1x(5x + 20) + -5 = 0.25(2x + 8)

Reorder the terms:
0.1x(20 + 5x) + -5 = 0.25(2x + 8)
(20 * 0.1x + 5x * 0.1x) + -5 = 0.25(2x + 8)
(2x + 0.5x2) + -5 = 0.25(2x + 8)

Reorder the terms:
-5 + 2x + 0.5x2 = 0.25(2x + 8)

Reorder the terms:
-5 + 2x + 0.5x2 = 0.25(8 + 2x)
-5 + 2x + 0.5x2 = (8 * 0.25 + 2x * 0.25)
-5 + 2x + 0.5x2 = (2 + 0.5x)

Solving
-5 + 2x + 0.5x2 = 2 + 0.5x

Solving for variable 'x'.

Reorder the terms:
-5 + -2 + 2x + -0.5x + 0.5x2 = 2 + 0.5x + -2 + -0.5x

Combine like terms: -5 + -2 = -7
-7 + 2x + -0.5x + 0.5x2 = 2 + 0.5x + -2 + -0.5x

Combine like terms: 2x + -0.5x = 1.5x
-7 + 1.5x + 0.5x2 = 2 + 0.5x + -2 + -0.5x

Reorder the terms:
-7 + 1.5x + 0.5x2 = 2 + -2 + 0.5x + -0.5x

Combine like terms: 2 + -2 = 0
-7 + 1.5x + 0.5x2 = 0 + 0.5x + -0.5x
-7 + 1.5x + 0.5x2 = 0.5x + -0.5x

Combine like terms: 0.5x + -0.5x = 0.0
-7 + 1.5x + 0.5x2 = 0.0

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

Divide each side by '0.5'.
-14 + 3x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 3x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 3x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 3x + x2 = 0 + 14
3x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
3x + x2 = 14

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 14 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 14 + 2.25

Combine like terms: 14 + 2.25 = 16.25
2.25 + 3x + x2 = 16.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
x + 1.5 = 4.031128874

Simplifying
x + 1.5 = 4.031128874

Reorder the terms:
1.5 + x = 4.031128874

Solving
1.5 + x = 4.031128874

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.031128874 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.031128874 + -1.5
x = 4.031128874 + -1.5

Combine like terms: 4.031128874 + -1.5 = 2.531128874
x = 2.531128874

Simplifying
x = 2.531128874

Subproblem 2
x + 1.5 = -4.031128874

Simplifying
x + 1.5 = -4.031128874

Reorder the terms:
1.5 + x = -4.031128874

Solving
1.5 + x = -4.031128874

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.031128874 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.031128874 + -1.5
x = -4.031128874 + -1.5

Combine like terms: -4.031128874 + -1.5 = -5.531128874
x = -5.531128874

Simplifying
x = -5.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.531128874, -5.531128874}