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

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

Simplifying
4(x + -1) * 2x = 2(x + 2)

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

Reorder the terms for easier multiplication:
4 * 2x(-1 + x) = 2(x + 2)

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

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

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

Solving for variable 'x'.

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

Combine like terms: -8x + -2x = -10x
-4 + -10x + 8x2 = 4 + 2x + -4 + -2x

Reorder the terms:
-4 + -10x + 8x2 = 4 + -4 + 2x + -2x

Combine like terms: 4 + -4 = 0
-4 + -10x + 8x2 = 0 + 2x + -2x
-4 + -10x + 8x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-4 + -10x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -5x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-2 + -5x + 4x2 = 0

Solving
-2 + -5x + 4x2 = 0

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

Divide each side by '4'.
-0.5 + -1.25x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.25x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.25x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.25x + x2 = 0 + 0.5
-1.25x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.25x + x2 = 0.5

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 0.5 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 0.5 + 0.390625

Combine like terms: 0.5 + 0.390625 = 0.890625
0.390625 + -1.25x + x2 = 0.890625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + -0.625) equal to 0.943729304 and -0.943729304.

Subproblem 1
x + -0.625 = 0.943729304

Simplifying
x + -0.625 = 0.943729304

Reorder the terms:
-0.625 + x = 0.943729304

Solving
-0.625 + x = 0.943729304

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 0.943729304 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 0.943729304 + 0.625
x = 0.943729304 + 0.625

Combine like terms: 0.943729304 + 0.625 = 1.568729304
x = 1.568729304

Simplifying
x = 1.568729304

Subproblem 2
x + -0.625 = -0.943729304

Simplifying
x + -0.625 = -0.943729304

Reorder the terms:
-0.625 + x = -0.943729304

Solving
-0.625 + x = -0.943729304

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -0.943729304 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -0.943729304 + 0.625
x = -0.943729304 + 0.625

Combine like terms: -0.943729304 + 0.625 = -0.318729304
x = -0.318729304

Simplifying
x = -0.318729304

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.568729304, -0.318729304}
Solution
x = {1.568729304, -0.318729304}