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

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

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

Reorder the terms:
-4x(8 + 2x) = 4x + -2
(8 * -4x + 2x * -4x) = 4x + -2
(-32x + -8x2) = 4x + -2

Reorder the terms:
-32x + -8x2 = -2 + 4x

Solving
-32x + -8x2 = -2 + 4x

Solving for variable 'x'.

Reorder the terms:
2 + -32x + -4x + -8x2 = -2 + 4x + 2 + -4x

Combine like terms: -32x + -4x = -36x
2 + -36x + -8x2 = -2 + 4x + 2 + -4x

Reorder the terms:
2 + -36x + -8x2 = -2 + 2 + 4x + -4x

Combine like terms: -2 + 2 = 0
2 + -36x + -8x2 = 0 + 4x + -4x
2 + -36x + -8x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
2 + -36x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -18x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -18x + -4x2)' equal to zero and attempt to solve:

Simplifying
1 + -18x + -4x2 = 0

Solving
1 + -18x + -4x2 = 0

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

Divide each side by '-4'.
-0.25 + 4.5x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 4.5x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 4.5x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 4.5x + x2 = 0 + 0.25
4.5x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
4.5x + x2 = 0.25

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 0.25 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 0.25 + 5.0625

Combine like terms: 0.25 + 5.0625 = 5.3125
5.0625 + 4.5x + x2 = 5.3125

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 5.3125

Calculate the square root of the right side: 2.304886114

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.304886114 and -2.304886114.

Subproblem 1
x + 2.25 = 2.304886114

Simplifying
x + 2.25 = 2.304886114

Reorder the terms:
2.25 + x = 2.304886114

Solving
2.25 + x = 2.304886114

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.304886114 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.304886114 + -2.25
x = 2.304886114 + -2.25

Combine like terms: 2.304886114 + -2.25 = 0.054886114
x = 0.054886114

Simplifying
x = 0.054886114

Subproblem 2
x + 2.25 = -2.304886114

Simplifying
x + 2.25 = -2.304886114

Reorder the terms:
2.25 + x = -2.304886114

Solving
2.25 + x = -2.304886114

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.304886114 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.304886114 + -2.25
x = -2.304886114 + -2.25

Combine like terms: -2.304886114 + -2.25 = -4.554886114
x = -4.554886114

Simplifying
x = -4.554886114

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.054886114, -4.554886114}
Solution
x = {0.054886114, -4.554886114}