5z(1-z)=0.8

Solution for 5z(1-z)=0.8 equation:

Simplifying
5z(1 + -1z) = 0.8
(1 * 5z + -1z * 5z) = 0.8
(5z + -5z2) = 0.8

Solving
5z + -5z2 = 0.8

Solving for variable 'z'.

Reorder the terms:
-0.8 + 5z + -5z2 = 0.8 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
-0.8 + 5z + -5z2 = 0.0

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

Divide each side by '-5'.
0.16 + -1z + z2 = 0.0

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -1z + -0.16 + z2 = 0.0 + -0.16

Reorder the terms:
0.16 + -0.16 + -1z + z2 = 0.0 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -1z + z2 = 0.0 + -0.16
-1z + z2 = 0.0 + -0.16

Combine like terms: 0.0 + -0.16 = -0.16
-1z + z2 = -0.16

The z term is -1z.  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.
-1z + 0.25 + z2 = -0.16 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -0.16 + 0.25

Combine like terms: -0.16 + 0.25 = 0.09
0.25 + -1z + z2 = 0.09

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = 0.09

Calculate the square root of the right side: 0.3

Break this problem into two subproblems by setting 
(z + -0.5) equal to 0.3 and -0.3.

Subproblem 1
z + -0.5 = 0.3

Simplifying
z + -0.5 = 0.3

Reorder the terms:
-0.5 + z = 0.3

Solving
-0.5 + z = 0.3

Solving for variable 'z'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + z = 0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + z = 0.3 + 0.5
z = 0.3 + 0.5

Combine like terms: 0.3 + 0.5 = 0.8
z = 0.8

Simplifying
z = 0.8

Subproblem 2
z + -0.5 = -0.3

Simplifying
z + -0.5 = -0.3

Reorder the terms:
-0.5 + z = -0.3

Solving
-0.5 + z = -0.3

Solving for variable 'z'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + z = -0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + z = -0.3 + 0.5
z = -0.3 + 0.5

Combine like terms: -0.3 + 0.5 = 0.2
z = 0.2

Simplifying
z = 0.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.8, 0.2}