(a-0.8)(a-0.2)=

Solution for (a-0.8)(a-0.2)= equation:

Simplifying
(a + -0.8)(a + -0.2) = 0

Reorder the terms:
(-0.8 + a)(a + -0.2) = 0

Reorder the terms:
(-0.8 + a)(-0.2 + a) = 0

Multiply (-0.8 + a) * (-0.2 + a)
(-0.8(-0.2 + a) + a(-0.2 + a)) = 0
((-0.2 * -0.8 + a * -0.8) + a(-0.2 + a)) = 0
((0.16 + -0.8a) + a(-0.2 + a)) = 0
(0.16 + -0.8a + (-0.2 * a + a * a)) = 0
(0.16 + -0.8a + (-0.2a + a2)) = 0

Combine like terms: -0.8a + -0.2a = -1a
(0.16 + -1a + a2) = 0

Solving
0.16 + -1a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -1a + -0.16 + a2 = 0 + -0.16

Reorder the terms:
0.16 + -0.16 + -1a + a2 = 0 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -1a + a2 = 0 + -0.16
-1a + a2 = 0 + -0.16

Combine like terms: 0 + -0.16 = -0.16
-1a + a2 = -0.16

The a term is -1a.  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.
-1a + 0.25 + a2 = -0.16 + 0.25

Reorder the terms:
0.25 + -1a + a2 = -0.16 + 0.25

Combine like terms: -0.16 + 0.25 = 0.09
0.25 + -1a + a2 = 0.09

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

Calculate the square root of the right side: 0.3

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

Subproblem 1
a + -0.5 = 0.3

Simplifying
a + -0.5 = 0.3

Reorder the terms:
-0.5 + a = 0.3

Solving
-0.5 + a = 0.3

Solving for variable 'a'.

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

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

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

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

Simplifying
a = 0.8

Subproblem 2
a + -0.5 = -0.3

Simplifying
a + -0.5 = -0.3

Reorder the terms:
-0.5 + a = -0.3

Solving
-0.5 + a = -0.3

Solving for variable 'a'.

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

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

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

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

Simplifying
a = 0.2

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