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

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

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

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

Reorder the terms for easier multiplication:
-4 * 2x(1 + x) = 2(x + 2) + -8 + -4x

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

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

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

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

Combine like terms: 2x + -4x = -2x
-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 = -6x
4 + -6x + -8x2 = -4 + -2x + 4 + 2x

Reorder the terms:
4 + -6x + -8x2 = -4 + 4 + -2x + 2x

Combine like terms: -4 + 4 = 0
4 + -6x + -8x2 = 0 + -2x + 2x
4 + -6x + -8x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
4 + -6x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -3x + -4x2)' equal to zero and attempt to solve:

Simplifying
2 + -3x + -4x2 = 0

Solving
2 + -3x + -4x2 = 0

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

Divide each side by '-4'.
-0.5 + 0.75x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.75x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.75x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.75x + x2 = 0 + 0.5
0.75x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.75x + x2 = 0.5

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 0.5 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 0.5 + 0.140625

Combine like terms: 0.5 + 0.140625 = 0.640625
0.140625 + 0.75x + x2 = 0.640625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(x + 0.375) equal to 0.80039053 and -0.80039053.

Subproblem 1
x + 0.375 = 0.80039053

Simplifying
x + 0.375 = 0.80039053

Reorder the terms:
0.375 + x = 0.80039053

Solving
0.375 + x = 0.80039053

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 0.80039053 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 0.80039053 + -0.375
x = 0.80039053 + -0.375

Combine like terms: 0.80039053 + -0.375 = 0.42539053
x = 0.42539053

Simplifying
x = 0.42539053

Subproblem 2
x + 0.375 = -0.80039053

Simplifying
x + 0.375 = -0.80039053

Reorder the terms:
0.375 + x = -0.80039053

Solving
0.375 + x = -0.80039053

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -0.80039053 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -0.80039053 + -0.375
x = -0.80039053 + -0.375

Combine like terms: -0.80039053 + -0.375 = -1.17539053
x = -1.17539053

Simplifying
x = -1.17539053

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.42539053, -1.17539053}
Solution
x = {0.42539053, -1.17539053}