0.5(0.2+x)=(0.32-2x)(0.2+x)

Solution for 0.5(0.2+x)=(0.32-2x)(0.2+x) equation:

Simplifying
0.5(0.2 + x) = (0.32 + -2x)(0.2 + x)
(0.2 * 0.5 + x * 0.5) = (0.32 + -2x)(0.2 + x)
(0.1 + 0.5x) = (0.32 + -2x)(0.2 + x)

Multiply (0.32 + -2x) * (0.2 + x)
0.1 + 0.5x = (0.32(0.2 + x) + -2x * (0.2 + x))
0.1 + 0.5x = ((0.2 * 0.32 + x * 0.32) + -2x * (0.2 + x))
0.1 + 0.5x = ((0.064 + 0.32x) + -2x * (0.2 + x))
0.1 + 0.5x = (0.064 + 0.32x + (0.2 * -2x + x * -2x))
0.1 + 0.5x = (0.064 + 0.32x + (-0.4x + -2x2))

Combine like terms: 0.32x + -0.4x = -0.08x
0.1 + 0.5x = (0.064 + -0.08x + -2x2)

Solving
0.1 + 0.5x = 0.064 + -0.08x + -2x2

Solving for variable 'x'.

Reorder the terms:
0.1 + -0.064 + 0.5x + 0.08x + 2x2 = 0.064 + -0.08x + -2x2 + -0.064 + 0.08x + 2x2

Combine like terms: 0.1 + -0.064 = 0.036
0.036 + 0.5x + 0.08x + 2x2 = 0.064 + -0.08x + -2x2 + -0.064 + 0.08x + 2x2

Combine like terms: 0.5x + 0.08x = 0.58x
0.036 + 0.58x + 2x2 = 0.064 + -0.08x + -2x2 + -0.064 + 0.08x + 2x2

Reorder the terms:
0.036 + 0.58x + 2x2 = 0.064 + -0.064 + -0.08x + 0.08x + -2x2 + 2x2

Combine like terms: 0.064 + -0.064 = 0.000
0.036 + 0.58x + 2x2 = 0.000 + -0.08x + 0.08x + -2x2 + 2x2
0.036 + 0.58x + 2x2 = -0.08x + 0.08x + -2x2 + 2x2

Combine like terms: -0.08x + 0.08x = 0.00
0.036 + 0.58x + 2x2 = 0.00 + -2x2 + 2x2
0.036 + 0.58x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
0.036 + 0.58x + 2x2 = 0

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

Divide each side by '2'.
0.018 + 0.29x + x2 = 0

Move the constant term to the right:

Add '-0.018' to each side of the equation.
0.018 + 0.29x + -0.018 + x2 = 0 + -0.018

Reorder the terms:
0.018 + -0.018 + 0.29x + x2 = 0 + -0.018

Combine like terms: 0.018 + -0.018 = 0.000
0.000 + 0.29x + x2 = 0 + -0.018
0.29x + x2 = 0 + -0.018

Combine like terms: 0 + -0.018 = -0.018
0.29x + x2 = -0.018

The x term is 0.29x.  Take half its coefficient (0.145).
Square it (0.021025) and add it to both sides.

Add '0.021025' to each side of the equation.
0.29x + 0.021025 + x2 = -0.018 + 0.021025

Reorder the terms:
0.021025 + 0.29x + x2 = -0.018 + 0.021025

Combine like terms: -0.018 + 0.021025 = 0.003025
0.021025 + 0.29x + x2 = 0.003025

Factor a perfect square on the left side:
(x + 0.145)(x + 0.145) = 0.003025

Calculate the square root of the right side: 0.055

Break this problem into two subproblems by setting 
(x + 0.145) equal to 0.055 and -0.055.

Subproblem 1
x + 0.145 = 0.055

Simplifying
x + 0.145 = 0.055

Reorder the terms:
0.145 + x = 0.055

Solving
0.145 + x = 0.055

Solving for variable 'x'.

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

Add '-0.145' to each side of the equation.
0.145 + -0.145 + x = 0.055 + -0.145

Combine like terms: 0.145 + -0.145 = 0.000
0.000 + x = 0.055 + -0.145
x = 0.055 + -0.145

Combine like terms: 0.055 + -0.145 = -0.09
x = -0.09

Simplifying
x = -0.09

Subproblem 2
x + 0.145 = -0.055

Simplifying
x + 0.145 = -0.055

Reorder the terms:
0.145 + x = -0.055

Solving
0.145 + x = -0.055

Solving for variable 'x'.

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

Add '-0.145' to each side of the equation.
0.145 + -0.145 + x = -0.055 + -0.145

Combine like terms: 0.145 + -0.145 = 0.000
0.000 + x = -0.055 + -0.145
x = -0.055 + -0.145

Combine like terms: -0.055 + -0.145 = -0.2
x = -0.2

Simplifying
x = -0.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.09, -0.2}