x(4x-2)+(4x-4)=(8x+3)(x-1)

Solution for x(4x-2)+(4x-4)=(8x+3)(x-1) equation:

Simplifying
x(4x + -2) + (4x + -4) = (8x + 3)(x + -1)

Reorder the terms:
x(-2 + 4x) + (4x + -4) = (8x + 3)(x + -1)
(-2 * x + 4x * x) + (4x + -4) = (8x + 3)(x + -1)
(-2x + 4x2) + (4x + -4) = (8x + 3)(x + -1)

Reorder the terms:
-2x + 4x2 + (-4 + 4x) = (8x + 3)(x + -1)

Remove parenthesis around (-4 + 4x)
-2x + 4x2 + -4 + 4x = (8x + 3)(x + -1)

Reorder the terms:
-4 + -2x + 4x + 4x2 = (8x + 3)(x + -1)

Combine like terms: -2x + 4x = 2x
-4 + 2x + 4x2 = (8x + 3)(x + -1)

Reorder the terms:
-4 + 2x + 4x2 = (3 + 8x)(x + -1)

Reorder the terms:
-4 + 2x + 4x2 = (3 + 8x)(-1 + x)

Multiply (3 + 8x) * (-1 + x)
-4 + 2x + 4x2 = (3(-1 + x) + 8x * (-1 + x))
-4 + 2x + 4x2 = ((-1 * 3 + x * 3) + 8x * (-1 + x))
-4 + 2x + 4x2 = ((-3 + 3x) + 8x * (-1 + x))
-4 + 2x + 4x2 = (-3 + 3x + (-1 * 8x + x * 8x))
-4 + 2x + 4x2 = (-3 + 3x + (-8x + 8x2))

Combine like terms: 3x + -8x = -5x
-4 + 2x + 4x2 = (-3 + -5x + 8x2)

Solving
-4 + 2x + 4x2 = -3 + -5x + 8x2

Solving for variable 'x'.

Reorder the terms:
-4 + 3 + 2x + 5x + 4x2 + -8x2 = -3 + -5x + 8x2 + 3 + 5x + -8x2

Combine like terms: -4 + 3 = -1
-1 + 2x + 5x + 4x2 + -8x2 = -3 + -5x + 8x2 + 3 + 5x + -8x2

Combine like terms: 2x + 5x = 7x
-1 + 7x + 4x2 + -8x2 = -3 + -5x + 8x2 + 3 + 5x + -8x2

Combine like terms: 4x2 + -8x2 = -4x2
-1 + 7x + -4x2 = -3 + -5x + 8x2 + 3 + 5x + -8x2

Reorder the terms:
-1 + 7x + -4x2 = -3 + 3 + -5x + 5x + 8x2 + -8x2

Combine like terms: -3 + 3 = 0
-1 + 7x + -4x2 = 0 + -5x + 5x + 8x2 + -8x2
-1 + 7x + -4x2 = -5x + 5x + 8x2 + -8x2

Combine like terms: -5x + 5x = 0
-1 + 7x + -4x2 = 0 + 8x2 + -8x2
-1 + 7x + -4x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-1 + 7x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -1.75x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.75x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.75x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.75x + x2 = 0 + -0.25
-1.75x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.75x + x2 = -0.25

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = -0.25 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = -0.25 + 0.765625

Combine like terms: -0.25 + 0.765625 = 0.515625
0.765625 + -1.75x + x2 = 0.515625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(x + -0.875) equal to 0.718070331 and -0.718070331.

Subproblem 1
x + -0.875 = 0.718070331

Simplifying
x + -0.875 = 0.718070331

Reorder the terms:
-0.875 + x = 0.718070331

Solving
-0.875 + x = 0.718070331

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 0.718070331 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 0.718070331 + 0.875
x = 0.718070331 + 0.875

Combine like terms: 0.718070331 + 0.875 = 1.593070331
x = 1.593070331

Simplifying
x = 1.593070331

Subproblem 2
x + -0.875 = -0.718070331

Simplifying
x + -0.875 = -0.718070331

Reorder the terms:
-0.875 + x = -0.718070331

Solving
-0.875 + x = -0.718070331

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -0.718070331 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -0.718070331 + 0.875
x = -0.718070331 + 0.875

Combine like terms: -0.718070331 + 0.875 = 0.156929669
x = 0.156929669

Simplifying
x = 0.156929669

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.593070331, 0.156929669}