0.8(5+5x)4x=20

Solution for 0.8(5+5x)4x=20 equation:

Simplifying
0.8(5 + 5x) * 4x = 20

Reorder the terms for easier multiplication:
0.8 * 4x(5 + 5x) = 20

Multiply 0.8 * 4
3.2x(5 + 5x) = 20
(5 * 3.2x + 5x * 3.2x) = 20
(16x + 16x2) = 20

Solving
16x + 16x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 16x + 16x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 4x + 4x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + 4x + 4x2)' equal to zero and attempt to solve:

Simplifying
-5 + 4x + 4x2 = 0

Solving
-5 + 4x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x + x2 = 0 + 1.25
x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
x + x2 = 1.25

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 1.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.25 + 0.25

Combine like terms: 1.25 + 0.25 = 1.5
1.25 + x2 = 1.5

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.224744871 and -1.224744871.

Subproblem 1
x + 0.5 = 1.224744871

Simplifying
x + 0.5 = 1.224744871

Reorder the terms:
0.5 + x = 1.224744871

Solving
0.5 + x = 1.224744871

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.224744871 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.224744871 + -0.5
x = 1.224744871 + -0.5

Combine like terms: 1.224744871 + -0.5 = 0.724744871
x = 0.724744871

Simplifying
x = 0.724744871

Subproblem 2
x + 0.5 = -1.224744871

Simplifying
x + 0.5 = -1.224744871

Reorder the terms:
0.5 + x = -1.224744871

Solving
0.5 + x = -1.224744871

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.224744871 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.224744871 + -0.5
x = -1.224744871 + -0.5

Combine like terms: -1.224744871 + -0.5 = -1.724744871
x = -1.724744871

Simplifying
x = -1.724744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.724744871, -1.724744871}
Solution
x = {0.724744871, -1.724744871}