0.025(0.6+2x)2=(0.2-x)(0.4-x)

Solution for 0.025(0.6+2x)2=(0.2-x)(0.4-x) equation:

Simplifying
0.025(0.6 + 2x) * 2 = (0.2 + -1x)(0.4 + -1x)

Reorder the terms for easier multiplication:
0.025 * 2(0.6 + 2x) = (0.2 + -1x)(0.4 + -1x)

Multiply 0.025 * 2
0.05(0.6 + 2x) = (0.2 + -1x)(0.4 + -1x)
(0.6 * 0.05 + 2x * 0.05) = (0.2 + -1x)(0.4 + -1x)
(0.03 + 0.1x) = (0.2 + -1x)(0.4 + -1x)

Multiply (0.2 + -1x) * (0.4 + -1x)
0.03 + 0.1x = (0.2(0.4 + -1x) + -1x * (0.4 + -1x))
0.03 + 0.1x = ((0.4 * 0.2 + -1x * 0.2) + -1x * (0.4 + -1x))
0.03 + 0.1x = ((0.08 + -0.2x) + -1x * (0.4 + -1x))
0.03 + 0.1x = (0.08 + -0.2x + (0.4 * -1x + -1x * -1x))
0.03 + 0.1x = (0.08 + -0.2x + (-0.4x + 1x2))

Combine like terms: -0.2x + -0.4x = -0.6x
0.03 + 0.1x = (0.08 + -0.6x + 1x2)

Solving
0.03 + 0.1x = 0.08 + -0.6x + 1x2

Solving for variable 'x'.

Reorder the terms:
0.03 + -0.08 + 0.1x + 0.6x + -1x2 = 0.08 + -0.6x + 1x2 + -0.08 + 0.6x + -1x2

Combine like terms: 0.03 + -0.08 = -0.05
-0.05 + 0.1x + 0.6x + -1x2 = 0.08 + -0.6x + 1x2 + -0.08 + 0.6x + -1x2

Combine like terms: 0.1x + 0.6x = 0.7x
-0.05 + 0.7x + -1x2 = 0.08 + -0.6x + 1x2 + -0.08 + 0.6x + -1x2

Reorder the terms:
-0.05 + 0.7x + -1x2 = 0.08 + -0.08 + -0.6x + 0.6x + 1x2 + -1x2

Combine like terms: 0.08 + -0.08 = 0.00
-0.05 + 0.7x + -1x2 = 0.00 + -0.6x + 0.6x + 1x2 + -1x2
-0.05 + 0.7x + -1x2 = -0.6x + 0.6x + 1x2 + -1x2

Combine like terms: -0.6x + 0.6x = 0.0
-0.05 + 0.7x + -1x2 = 0.0 + 1x2 + -1x2
-0.05 + 0.7x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-0.05 + 0.7x + -1x2 = 0

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

Divide each side by '-1'.
0.05 + -0.7x + x2 = 0

Move the constant term to the right:

Add '-0.05' to each side of the equation.
0.05 + -0.7x + -0.05 + x2 = 0 + -0.05

Reorder the terms:
0.05 + -0.05 + -0.7x + x2 = 0 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + -0.7x + x2 = 0 + -0.05
-0.7x + x2 = 0 + -0.05

Combine like terms: 0 + -0.05 = -0.05
-0.7x + x2 = -0.05

The x term is -0.7x.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7x + 0.1225 + x2 = -0.05 + 0.1225

Reorder the terms:
0.1225 + -0.7x + x2 = -0.05 + 0.1225

Combine like terms: -0.05 + 0.1225 = 0.0725
0.1225 + -0.7x + x2 = 0.0725

Factor a perfect square on the left side:
(x + -0.35)(x + -0.35) = 0.0725

Calculate the square root of the right side: 0.26925824

Break this problem into two subproblems by setting 
(x + -0.35) equal to 0.26925824 and -0.26925824.

Subproblem 1
x + -0.35 = 0.26925824

Simplifying
x + -0.35 = 0.26925824

Reorder the terms:
-0.35 + x = 0.26925824

Solving
-0.35 + x = 0.26925824

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = 0.26925824 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = 0.26925824 + 0.35
x = 0.26925824 + 0.35

Combine like terms: 0.26925824 + 0.35 = 0.61925824
x = 0.61925824

Simplifying
x = 0.61925824

Subproblem 2
x + -0.35 = -0.26925824

Simplifying
x + -0.35 = -0.26925824

Reorder the terms:
-0.35 + x = -0.26925824

Solving
-0.35 + x = -0.26925824

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = -0.26925824 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = -0.26925824 + 0.35
x = -0.26925824 + 0.35

Combine like terms: -0.26925824 + 0.35 = 0.08074176
x = 0.08074176

Simplifying
x = 0.08074176

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.61925824, 0.08074176}