0.9(2x-1)(1+x)=0.2(x)(1-x)

Solution for 0.9(2x-1)(1+x)=0.2(x)(1-x) equation:

Simplifying
0.9(2x + -1)(1 + x) = 0.2(x)(1 + -1x)

Reorder the terms:
0.9(-1 + 2x)(1 + x) = 0.2(x)(1 + -1x)

Multiply (-1 + 2x) * (1 + x)
0.9(-1(1 + x) + 2x * (1 + x)) = 0.2(x)(1 + -1x)
0.9((1 * -1 + x * -1) + 2x * (1 + x)) = 0.2(x)(1 + -1x)
0.9((-1 + -1x) + 2x * (1 + x)) = 0.2(x)(1 + -1x)
0.9(-1 + -1x + (1 * 2x + x * 2x)) = 0.2(x)(1 + -1x)
0.9(-1 + -1x + (2x + 2x2)) = 0.2(x)(1 + -1x)

Combine like terms: -1x + 2x = 1x
0.9(-1 + 1x + 2x2) = 0.2(x)(1 + -1x)
(-1 * 0.9 + 1x * 0.9 + 2x2 * 0.9) = 0.2(x)(1 + -1x)
(-0.9 + 0.9x + 1.8x2) = 0.2(x)(1 + -1x)
-0.9 + 0.9x + 1.8x2 = (1 * 0.2x + -1x * 0.2x)
-0.9 + 0.9x + 1.8x2 = (0.2x + -0.2x2)

Solving
-0.9 + 0.9x + 1.8x2 = 0.2x + -0.2x2

Solving for variable 'x'.

Reorder the terms:
-0.9 + 0.9x + -0.2x + 1.8x2 + 0.2x2 = 0.2x + -0.2x2 + -0.2x + 0.2x2

Combine like terms: 0.9x + -0.2x = 0.7x
-0.9 + 0.7x + 1.8x2 + 0.2x2 = 0.2x + -0.2x2 + -0.2x + 0.2x2

Combine like terms: 1.8x2 + 0.2x2 = 2x2
-0.9 + 0.7x + 2x2 = 0.2x + -0.2x2 + -0.2x + 0.2x2

Reorder the terms:
-0.9 + 0.7x + 2x2 = 0.2x + -0.2x + -0.2x2 + 0.2x2

Combine like terms: 0.2x + -0.2x = 0.0
-0.9 + 0.7x + 2x2 = 0.0 + -0.2x2 + 0.2x2
-0.9 + 0.7x + 2x2 = -0.2x2 + 0.2x2

Combine like terms: -0.2x2 + 0.2x2 = 0.0
-0.9 + 0.7x + 2x2 = 0.0

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

Divide each side by '2'.
-0.45 + 0.35x + x2 = 0.0

Move the constant term to the right:

Add '0.45' to each side of the equation.
-0.45 + 0.35x + 0.45 + x2 = 0.0 + 0.45

Reorder the terms:
-0.45 + 0.45 + 0.35x + x2 = 0.0 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + 0.35x + x2 = 0.0 + 0.45
0.35x + x2 = 0.0 + 0.45

Combine like terms: 0.0 + 0.45 = 0.45
0.35x + x2 = 0.45

The x term is 0.35x.  Take half its coefficient (0.175).
Square it (0.030625) and add it to both sides.

Add '0.030625' to each side of the equation.
0.35x + 0.030625 + x2 = 0.45 + 0.030625

Reorder the terms:
0.030625 + 0.35x + x2 = 0.45 + 0.030625

Combine like terms: 0.45 + 0.030625 = 0.480625
0.030625 + 0.35x + x2 = 0.480625

Factor a perfect square on the left side:
(x + 0.175)(x + 0.175) = 0.480625

Calculate the square root of the right side: 0.693271231

Break this problem into two subproblems by setting 
(x + 0.175) equal to 0.693271231 and -0.693271231.

Subproblem 1
x + 0.175 = 0.693271231

Simplifying
x + 0.175 = 0.693271231

Reorder the terms:
0.175 + x = 0.693271231

Solving
0.175 + x = 0.693271231

Solving for variable 'x'.

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

Add '-0.175' to each side of the equation.
0.175 + -0.175 + x = 0.693271231 + -0.175

Combine like terms: 0.175 + -0.175 = 0.000
0.000 + x = 0.693271231 + -0.175
x = 0.693271231 + -0.175

Combine like terms: 0.693271231 + -0.175 = 0.518271231
x = 0.518271231

Simplifying
x = 0.518271231

Subproblem 2
x + 0.175 = -0.693271231

Simplifying
x + 0.175 = -0.693271231

Reorder the terms:
0.175 + x = -0.693271231

Solving
0.175 + x = -0.693271231

Solving for variable 'x'.

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

Add '-0.175' to each side of the equation.
0.175 + -0.175 + x = -0.693271231 + -0.175

Combine like terms: 0.175 + -0.175 = 0.000
0.000 + x = -0.693271231 + -0.175
x = -0.693271231 + -0.175

Combine like terms: -0.693271231 + -0.175 = -0.868271231
x = -0.868271231

Simplifying
x = -0.868271231

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.518271231, -0.868271231}