(0.8-2x)(0.8-2x)=.74(0.1+x)(0.4+x)

Solution for (0.8-2x)(0.8-2x)=.74(0.1+x)(0.4+x) equation:

Simplifying
(0.8 + -2x)(0.8 + -2x) = 0.74(0.1 + x)(0.4 + x)

Multiply (0.8 + -2x) * (0.8 + -2x)
(0.8(0.8 + -2x) + -2x * (0.8 + -2x)) = 0.74(0.1 + x)(0.4 + x)
((0.8 * 0.8 + -2x * 0.8) + -2x * (0.8 + -2x)) = 0.74(0.1 + x)(0.4 + x)
((0.64 + -1.6x) + -2x * (0.8 + -2x)) = 0.74(0.1 + x)(0.4 + x)
(0.64 + -1.6x + (0.8 * -2x + -2x * -2x)) = 0.74(0.1 + x)(0.4 + x)
(0.64 + -1.6x + (-1.6x + 4x2)) = 0.74(0.1 + x)(0.4 + x)

Combine like terms: -1.6x + -1.6x = -3.2x
(0.64 + -3.2x + 4x2) = 0.74(0.1 + x)(0.4 + x)

Multiply (0.1 + x) * (0.4 + x)
0.64 + -3.2x + 4x2 = 0.74(0.1(0.4 + x) + x(0.4 + x))
0.64 + -3.2x + 4x2 = 0.74((0.4 * 0.1 + x * 0.1) + x(0.4 + x))
0.64 + -3.2x + 4x2 = 0.74((0.04 + 0.1x) + x(0.4 + x))
0.64 + -3.2x + 4x2 = 0.74(0.04 + 0.1x + (0.4 * x + x * x))
0.64 + -3.2x + 4x2 = 0.74(0.04 + 0.1x + (0.4x + x2))

Combine like terms: 0.1x + 0.4x = 0.5x
0.64 + -3.2x + 4x2 = 0.74(0.04 + 0.5x + x2)
0.64 + -3.2x + 4x2 = (0.04 * 0.74 + 0.5x * 0.74 + x2 * 0.74)
0.64 + -3.2x + 4x2 = (0.0296 + 0.37x + 0.74x2)

Solving
0.64 + -3.2x + 4x2 = 0.0296 + 0.37x + 0.74x2

Solving for variable 'x'.

Reorder the terms:
0.64 + -0.0296 + -3.2x + -0.37x + 4x2 + -0.74x2 = 0.0296 + 0.37x + 0.74x2 + -0.0296 + -0.37x + -0.74x2

Combine like terms: 0.64 + -0.0296 = 0.6104
0.6104 + -3.2x + -0.37x + 4x2 + -0.74x2 = 0.0296 + 0.37x + 0.74x2 + -0.0296 + -0.37x + -0.74x2

Combine like terms: -3.2x + -0.37x = -3.57x
0.6104 + -3.57x + 4x2 + -0.74x2 = 0.0296 + 0.37x + 0.74x2 + -0.0296 + -0.37x + -0.74x2

Combine like terms: 4x2 + -0.74x2 = 3.26x2
0.6104 + -3.57x + 3.26x2 = 0.0296 + 0.37x + 0.74x2 + -0.0296 + -0.37x + -0.74x2

Reorder the terms:
0.6104 + -3.57x + 3.26x2 = 0.0296 + -0.0296 + 0.37x + -0.37x + 0.74x2 + -0.74x2

Combine like terms: 0.0296 + -0.0296 = 0.0000
0.6104 + -3.57x + 3.26x2 = 0.0000 + 0.37x + -0.37x + 0.74x2 + -0.74x2
0.6104 + -3.57x + 3.26x2 = 0.37x + -0.37x + 0.74x2 + -0.74x2

Combine like terms: 0.37x + -0.37x = 0.00
0.6104 + -3.57x + 3.26x2 = 0.00 + 0.74x2 + -0.74x2
0.6104 + -3.57x + 3.26x2 = 0.74x2 + -0.74x2

Combine like terms: 0.74x2 + -0.74x2 = 0.00
0.6104 + -3.57x + 3.26x2 = 0.00

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

Divide each side by '3.26'.
0.1872392638 + -1.095092025x + x2 = 0

Move the constant term to the right:

Add '-0.1872392638' to each side of the equation.
0.1872392638 + -1.095092025x + -0.1872392638 + x2 = 0 + -0.1872392638

Reorder the terms:
0.1872392638 + -0.1872392638 + -1.095092025x + x2 = 0 + -0.1872392638

Combine like terms: 0.1872392638 + -0.1872392638 = 0.0000000000
0.0000000000 + -1.095092025x + x2 = 0 + -0.1872392638
-1.095092025x + x2 = 0 + -0.1872392638

Combine like terms: 0 + -0.1872392638 = -0.1872392638
-1.095092025x + x2 = -0.1872392638

The x term is -1.095092025x.  Take half its coefficient (-0.5475460125).
Square it (0.2998066358) and add it to both sides.

Add '0.2998066358' to each side of the equation.
-1.095092025x + 0.2998066358 + x2 = -0.1872392638 + 0.2998066358

Reorder the terms:
0.2998066358 + -1.095092025x + x2 = -0.1872392638 + 0.2998066358

Combine like terms: -0.1872392638 + 0.2998066358 = 0.112567372
0.2998066358 + -1.095092025x + x2 = 0.112567372

Factor a perfect square on the left side:
(x + -0.5475460125)(x + -0.5475460125) = 0.112567372

Calculate the square root of the right side: 0.335510614

Break this problem into two subproblems by setting 
(x + -0.5475460125) equal to 0.335510614 and -0.335510614.

Subproblem 1
x + -0.5475460125 = 0.335510614

Simplifying
x + -0.5475460125 = 0.335510614

Reorder the terms:
-0.5475460125 + x = 0.335510614

Solving
-0.5475460125 + x = 0.335510614

Solving for variable 'x'.

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

Add '0.5475460125' to each side of the equation.
-0.5475460125 + 0.5475460125 + x = 0.335510614 + 0.5475460125

Combine like terms: -0.5475460125 + 0.5475460125 = 0.0000000000
0.0000000000 + x = 0.335510614 + 0.5475460125
x = 0.335510614 + 0.5475460125

Combine like terms: 0.335510614 + 0.5475460125 = 0.8830566265
x = 0.8830566265

Simplifying
x = 0.8830566265

Subproblem 2
x + -0.5475460125 = -0.335510614

Simplifying
x + -0.5475460125 = -0.335510614

Reorder the terms:
-0.5475460125 + x = -0.335510614

Solving
-0.5475460125 + x = -0.335510614

Solving for variable 'x'.

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

Add '0.5475460125' to each side of the equation.
-0.5475460125 + 0.5475460125 + x = -0.335510614 + 0.5475460125

Combine like terms: -0.5475460125 + 0.5475460125 = 0.0000000000
0.0000000000 + x = -0.335510614 + 0.5475460125
x = -0.335510614 + 0.5475460125

Combine like terms: -0.335510614 + 0.5475460125 = 0.2120353985
x = 0.2120353985

Simplifying
x = 0.2120353985

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8830566265, 0.2120353985}