(6.41)(1.2-x)(-x)=(8+2x)(8+2x)

Solution for (6.41)(1.2-x)(-x)=(8+2x)(8+2x) equation:

Simplifying
(6.41)(1.2 + -1x)(-1x) = (8 + 2x)(8 + 2x)

Remove parenthesis around (-1x)
6.41(1.2 + -1x) * -1x = (8 + 2x)(8 + 2x)

Reorder the terms for easier multiplication:
6.41 * -1x(1.2 + -1x) = (8 + 2x)(8 + 2x)

Multiply 6.41 * -1
-6.41x(1.2 + -1x) = (8 + 2x)(8 + 2x)
(1.2 * -6.41x + -1x * -6.41x) = (8 + 2x)(8 + 2x)
(-7.692x + 6.41x2) = (8 + 2x)(8 + 2x)

Multiply (8 + 2x) * (8 + 2x)
-7.692x + 6.41x2 = (8(8 + 2x) + 2x * (8 + 2x))
-7.692x + 6.41x2 = ((8 * 8 + 2x * 8) + 2x * (8 + 2x))
-7.692x + 6.41x2 = ((64 + 16x) + 2x * (8 + 2x))
-7.692x + 6.41x2 = (64 + 16x + (8 * 2x + 2x * 2x))
-7.692x + 6.41x2 = (64 + 16x + (16x + 4x2))

Combine like terms: 16x + 16x = 32x
-7.692x + 6.41x2 = (64 + 32x + 4x2)

Solving
-7.692x + 6.41x2 = 64 + 32x + 4x2

Solving for variable 'x'.

Reorder the terms:
-64 + -7.692x + -32x + 6.41x2 + -4x2 = 64 + 32x + 4x2 + -64 + -32x + -4x2

Combine like terms: -7.692x + -32x = -39.692x
-64 + -39.692x + 6.41x2 + -4x2 = 64 + 32x + 4x2 + -64 + -32x + -4x2

Combine like terms: 6.41x2 + -4x2 = 2.41x2
-64 + -39.692x + 2.41x2 = 64 + 32x + 4x2 + -64 + -32x + -4x2

Reorder the terms:
-64 + -39.692x + 2.41x2 = 64 + -64 + 32x + -32x + 4x2 + -4x2

Combine like terms: 64 + -64 = 0
-64 + -39.692x + 2.41x2 = 0 + 32x + -32x + 4x2 + -4x2
-64 + -39.692x + 2.41x2 = 32x + -32x + 4x2 + -4x2

Combine like terms: 32x + -32x = 0
-64 + -39.692x + 2.41x2 = 0 + 4x2 + -4x2
-64 + -39.692x + 2.41x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-64 + -39.692x + 2.41x2 = 0

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

Divide each side by '2.41'.
-26.5560166 + -16.46970954x + x2 = 0

Move the constant term to the right:

Add '26.5560166' to each side of the equation.
-26.5560166 + -16.46970954x + 26.5560166 + x2 = 0 + 26.5560166

Reorder the terms:
-26.5560166 + 26.5560166 + -16.46970954x + x2 = 0 + 26.5560166

Combine like terms: -26.5560166 + 26.5560166 = 0.0000000
0.0000000 + -16.46970954x + x2 = 0 + 26.5560166
-16.46970954x + x2 = 0 + 26.5560166

Combine like terms: 0 + 26.5560166 = 26.5560166
-16.46970954x + x2 = 26.5560166

The x term is -16.46970954x.  Take half its coefficient (-8.23485477).
Square it (67.81283308) and add it to both sides.

Add '67.81283308' to each side of the equation.
-16.46970954x + 67.81283308 + x2 = 26.5560166 + 67.81283308

Reorder the terms:
67.81283308 + -16.46970954x + x2 = 26.5560166 + 67.81283308

Combine like terms: 26.5560166 + 67.81283308 = 94.36884968
67.81283308 + -16.46970954x + x2 = 94.36884968

Factor a perfect square on the left side:
(x + -8.23485477)(x + -8.23485477) = 94.36884968

Calculate the square root of the right side: 9.714363061

Break this problem into two subproblems by setting 
(x + -8.23485477) equal to 9.714363061 and -9.714363061.

Subproblem 1
x + -8.23485477 = 9.714363061

Simplifying
x + -8.23485477 = 9.714363061

Reorder the terms:
-8.23485477 + x = 9.714363061

Solving
-8.23485477 + x = 9.714363061

Solving for variable 'x'.

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

Add '8.23485477' to each side of the equation.
-8.23485477 + 8.23485477 + x = 9.714363061 + 8.23485477

Combine like terms: -8.23485477 + 8.23485477 = 0.00000000
0.00000000 + x = 9.714363061 + 8.23485477
x = 9.714363061 + 8.23485477

Combine like terms: 9.714363061 + 8.23485477 = 17.949217831
x = 17.949217831

Simplifying
x = 17.949217831

Subproblem 2
x + -8.23485477 = -9.714363061

Simplifying
x + -8.23485477 = -9.714363061

Reorder the terms:
-8.23485477 + x = -9.714363061

Solving
-8.23485477 + x = -9.714363061

Solving for variable 'x'.

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

Add '8.23485477' to each side of the equation.
-8.23485477 + 8.23485477 + x = -9.714363061 + 8.23485477

Combine like terms: -8.23485477 + 8.23485477 = 0.00000000
0.00000000 + x = -9.714363061 + 8.23485477
x = -9.714363061 + 8.23485477

Combine like terms: -9.714363061 + 8.23485477 = -1.479508291
x = -1.479508291

Simplifying
x = -1.479508291

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.949217831, -1.479508291}