0.25(0.6+2x)=(0.2-x)(0.4-x)

Solution for 0.25(0.6+2x)=(0.2-x)(0.4-x) equation:

Simplifying
0.25(0.6 + 2x) = (0.2 + -1x)(0.4 + -1x)
(0.6 * 0.25 + 2x * 0.25) = (0.2 + -1x)(0.4 + -1x)
(0.15 + 0.5x) = (0.2 + -1x)(0.4 + -1x)

Multiply (0.2 + -1x) * (0.4 + -1x)
0.15 + 0.5x = (0.2(0.4 + -1x) + -1x * (0.4 + -1x))
0.15 + 0.5x = ((0.4 * 0.2 + -1x * 0.2) + -1x * (0.4 + -1x))
0.15 + 0.5x = ((0.08 + -0.2x) + -1x * (0.4 + -1x))
0.15 + 0.5x = (0.08 + -0.2x + (0.4 * -1x + -1x * -1x))
0.15 + 0.5x = (0.08 + -0.2x + (-0.4x + 1x2))

Combine like terms: -0.2x + -0.4x = -0.6x
0.15 + 0.5x = (0.08 + -0.6x + 1x2)

Solving
0.15 + 0.5x = 0.08 + -0.6x + 1x2

Solving for variable 'x'.

Reorder the terms:
0.15 + -0.08 + 0.5x + 0.6x + -1x2 = 0.08 + -0.6x + 1x2 + -0.08 + 0.6x + -1x2

Combine like terms: 0.15 + -0.08 = 0.07
0.07 + 0.5x + 0.6x + -1x2 = 0.08 + -0.6x + 1x2 + -0.08 + 0.6x + -1x2

Combine like terms: 0.5x + 0.6x = 1.1x
0.07 + 1.1x + -1x2 = 0.08 + -0.6x + 1x2 + -0.08 + 0.6x + -1x2

Reorder the terms:
0.07 + 1.1x + -1x2 = 0.08 + -0.08 + -0.6x + 0.6x + 1x2 + -1x2

Combine like terms: 0.08 + -0.08 = 0.00
0.07 + 1.1x + -1x2 = 0.00 + -0.6x + 0.6x + 1x2 + -1x2
0.07 + 1.1x + -1x2 = -0.6x + 0.6x + 1x2 + -1x2

Combine like terms: -0.6x + 0.6x = 0.0
0.07 + 1.1x + -1x2 = 0.0 + 1x2 + -1x2
0.07 + 1.1x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
0.07 + 1.1x + -1x2 = 0

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

Divide each side by '-1'.
-0.07 + -1.1x + x2 = 0

Move the constant term to the right:

Add '0.07' to each side of the equation.
-0.07 + -1.1x + 0.07 + x2 = 0 + 0.07

Reorder the terms:
-0.07 + 0.07 + -1.1x + x2 = 0 + 0.07

Combine like terms: -0.07 + 0.07 = 0.00
0.00 + -1.1x + x2 = 0 + 0.07
-1.1x + x2 = 0 + 0.07

Combine like terms: 0 + 0.07 = 0.07
-1.1x + x2 = 0.07

The x term is -1.1x.  Take half its coefficient (-0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
-1.1x + 0.3025 + x2 = 0.07 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = 0.07 + 0.3025

Combine like terms: 0.07 + 0.3025 = 0.3725
0.3025 + -1.1x + x2 = 0.3725

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = 0.3725

Calculate the square root of the right side: 0.610327781

Break this problem into two subproblems by setting 
(x + -0.55) equal to 0.610327781 and -0.610327781.

Subproblem 1
x + -0.55 = 0.610327781

Simplifying
x + -0.55 = 0.610327781

Reorder the terms:
-0.55 + x = 0.610327781

Solving
-0.55 + x = 0.610327781

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = 0.610327781 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = 0.610327781 + 0.55
x = 0.610327781 + 0.55

Combine like terms: 0.610327781 + 0.55 = 1.160327781
x = 1.160327781

Simplifying
x = 1.160327781

Subproblem 2
x + -0.55 = -0.610327781

Simplifying
x + -0.55 = -0.610327781

Reorder the terms:
-0.55 + x = -0.610327781

Solving
-0.55 + x = -0.610327781

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = -0.610327781 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = -0.610327781 + 0.55
x = -0.610327781 + 0.55

Combine like terms: -0.610327781 + 0.55 = -0.060327781
x = -0.060327781

Simplifying
x = -0.060327781

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.160327781, -0.060327781}