((0.3-x)(0.3-x))=0.2x(0.2+x)

Solution for ((0.3-x)(0.3-x))=0.2x(0.2+x) equation:

Simplifying
((0.3 + -1x)(0.3 + -1x)) = 0.2x(0.2 + x)

Multiply (0.3 + -1x) * (0.3 + -1x)
((0.3(0.3 + -1x) + -1x * (0.3 + -1x))) = 0.2x(0.2 + x)
(((0.3 * 0.3 + -1x * 0.3) + -1x * (0.3 + -1x))) = 0.2x(0.2 + x)
(((0.09 + -0.3x) + -1x * (0.3 + -1x))) = 0.2x(0.2 + x)
((0.09 + -0.3x + (0.3 * -1x + -1x * -1x))) = 0.2x(0.2 + x)
((0.09 + -0.3x + (-0.3x + 1x2))) = 0.2x(0.2 + x)

Combine like terms: -0.3x + -0.3x = -0.6x
((0.09 + -0.6x + 1x2)) = 0.2x(0.2 + x)
(0.09 + -0.6x + 1x2) = 0.2x(0.2 + x)

Remove parenthesis around (0.09 + -0.6x + 1x2)
0.09 + -0.6x + 1x2 = 0.2x(0.2 + x)
0.09 + -0.6x + 1x2 = (0.2 * 0.2x + x * 0.2x)
0.09 + -0.6x + 1x2 = (0.04x + 0.2x2)

Solving
0.09 + -0.6x + 1x2 = 0.04x + 0.2x2

Solving for variable 'x'.

Reorder the terms:
0.09 + -0.6x + -0.04x + 1x2 + -0.2x2 = 0.04x + 0.2x2 + -0.04x + -0.2x2

Combine like terms: -0.6x + -0.04x = -0.64x
0.09 + -0.64x + 1x2 + -0.2x2 = 0.04x + 0.2x2 + -0.04x + -0.2x2

Combine like terms: 1x2 + -0.2x2 = 0.8x2
0.09 + -0.64x + 0.8x2 = 0.04x + 0.2x2 + -0.04x + -0.2x2

Reorder the terms:
0.09 + -0.64x + 0.8x2 = 0.04x + -0.04x + 0.2x2 + -0.2x2

Combine like terms: 0.04x + -0.04x = 0.00
0.09 + -0.64x + 0.8x2 = 0.00 + 0.2x2 + -0.2x2
0.09 + -0.64x + 0.8x2 = 0.2x2 + -0.2x2

Combine like terms: 0.2x2 + -0.2x2 = 0.0
0.09 + -0.64x + 0.8x2 = 0.0

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

Divide each side by '0.8'.
0.1125 + -0.8x + x2 = 0

Move the constant term to the right:

Add '-0.1125' to each side of the equation.
0.1125 + -0.8x + -0.1125 + x2 = 0 + -0.1125

Reorder the terms:
0.1125 + -0.1125 + -0.8x + x2 = 0 + -0.1125

Combine like terms: 0.1125 + -0.1125 = 0.0000
0.0000 + -0.8x + x2 = 0 + -0.1125
-0.8x + x2 = 0 + -0.1125

Combine like terms: 0 + -0.1125 = -0.1125
-0.8x + x2 = -0.1125

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = -0.1125 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = -0.1125 + 0.16

Combine like terms: -0.1125 + 0.16 = 0.0475
0.16 + -0.8x + x2 = 0.0475

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.0475

Calculate the square root of the right side: 0.217944947

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.217944947 and -0.217944947.

Subproblem 1
x + -0.4 = 0.217944947

Simplifying
x + -0.4 = 0.217944947

Reorder the terms:
-0.4 + x = 0.217944947

Solving
-0.4 + x = 0.217944947

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 0.217944947 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 0.217944947 + 0.4
x = 0.217944947 + 0.4

Combine like terms: 0.217944947 + 0.4 = 0.617944947
x = 0.617944947

Simplifying
x = 0.617944947

Subproblem 2
x + -0.4 = -0.217944947

Simplifying
x + -0.4 = -0.217944947

Reorder the terms:
-0.4 + x = -0.217944947

Solving
-0.4 + x = -0.217944947

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -0.217944947 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -0.217944947 + 0.4
x = -0.217944947 + 0.4

Combine like terms: -0.217944947 + 0.4 = 0.182055053
x = 0.182055053

Simplifying
x = 0.182055053

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.617944947, 0.182055053}