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

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

Simplifying
0.025(0.6 + 2x) = (0.2 + -1x)(0.4 + -1x)
(0.6 * 0.025 + 2x * 0.025) = (0.2 + -1x)(0.4 + -1x)
(0.015 + 0.05x) = (0.2 + -1x)(0.4 + -1x)

Multiply (0.2 + -1x) * (0.4 + -1x)
0.015 + 0.05x = (0.2(0.4 + -1x) + -1x * (0.4 + -1x))
0.015 + 0.05x = ((0.4 * 0.2 + -1x * 0.2) + -1x * (0.4 + -1x))
0.015 + 0.05x = ((0.08 + -0.2x) + -1x * (0.4 + -1x))
0.015 + 0.05x = (0.08 + -0.2x + (0.4 * -1x + -1x * -1x))
0.015 + 0.05x = (0.08 + -0.2x + (-0.4x + 1x2))

Combine like terms: -0.2x + -0.4x = -0.6x
0.015 + 0.05x = (0.08 + -0.6x + 1x2)

Solving
0.015 + 0.05x = 0.08 + -0.6x + 1x2

Solving for variable 'x'.

Reorder the terms:
0.015 + -0.08 + 0.05x + 0.6x + -1x2 = 0.08 + -0.6x + 1x2 + -0.08 + 0.6x + -1x2

Combine like terms: 0.015 + -0.08 = -0.065
-0.065 + 0.05x + 0.6x + -1x2 = 0.08 + -0.6x + 1x2 + -0.08 + 0.6x + -1x2

Combine like terms: 0.05x + 0.6x = 0.65x
-0.065 + 0.65x + -1x2 = 0.08 + -0.6x + 1x2 + -0.08 + 0.6x + -1x2

Reorder the terms:
-0.065 + 0.65x + -1x2 = 0.08 + -0.08 + -0.6x + 0.6x + 1x2 + -1x2

Combine like terms: 0.08 + -0.08 = 0.00
-0.065 + 0.65x + -1x2 = 0.00 + -0.6x + 0.6x + 1x2 + -1x2
-0.065 + 0.65x + -1x2 = -0.6x + 0.6x + 1x2 + -1x2

Combine like terms: -0.6x + 0.6x = 0.0
-0.065 + 0.65x + -1x2 = 0.0 + 1x2 + -1x2
-0.065 + 0.65x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-0.065 + 0.65x + -1x2 = 0

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

Divide each side by '-1'.
0.065 + -0.65x + x2 = 0

Move the constant term to the right:

Add '-0.065' to each side of the equation.
0.065 + -0.65x + -0.065 + x2 = 0 + -0.065

Reorder the terms:
0.065 + -0.065 + -0.65x + x2 = 0 + -0.065

Combine like terms: 0.065 + -0.065 = 0.000
0.000 + -0.65x + x2 = 0 + -0.065
-0.65x + x2 = 0 + -0.065

Combine like terms: 0 + -0.065 = -0.065
-0.65x + x2 = -0.065

The x term is -0.65x.  Take half its coefficient (-0.325).
Square it (0.105625) and add it to both sides.

Add '0.105625' to each side of the equation.
-0.65x + 0.105625 + x2 = -0.065 + 0.105625

Reorder the terms:
0.105625 + -0.65x + x2 = -0.065 + 0.105625

Combine like terms: -0.065 + 0.105625 = 0.040625
0.105625 + -0.65x + x2 = 0.040625

Factor a perfect square on the left side:
(x + -0.325)(x + -0.325) = 0.040625

Calculate the square root of the right side: 0.201556444

Break this problem into two subproblems by setting 
(x + -0.325) equal to 0.201556444 and -0.201556444.

Subproblem 1
x + -0.325 = 0.201556444

Simplifying
x + -0.325 = 0.201556444

Reorder the terms:
-0.325 + x = 0.201556444

Solving
-0.325 + x = 0.201556444

Solving for variable 'x'.

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

Add '0.325' to each side of the equation.
-0.325 + 0.325 + x = 0.201556444 + 0.325

Combine like terms: -0.325 + 0.325 = 0.000
0.000 + x = 0.201556444 + 0.325
x = 0.201556444 + 0.325

Combine like terms: 0.201556444 + 0.325 = 0.526556444
x = 0.526556444

Simplifying
x = 0.526556444

Subproblem 2
x + -0.325 = -0.201556444

Simplifying
x + -0.325 = -0.201556444

Reorder the terms:
-0.325 + x = -0.201556444

Solving
-0.325 + x = -0.201556444

Solving for variable 'x'.

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

Add '0.325' to each side of the equation.
-0.325 + 0.325 + x = -0.201556444 + 0.325

Combine like terms: -0.325 + 0.325 = 0.000
0.000 + x = -0.201556444 + 0.325
x = -0.201556444 + 0.325

Combine like terms: -0.201556444 + 0.325 = 0.123443556
x = 0.123443556

Simplifying
x = 0.123443556

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.526556444, 0.123443556}