-2x(x-8)+4x=-12

Solution for -2x(x-8)+4x=-12 equation:

Simplifying
-2x(x + -8) + 4x = -12

Reorder the terms:
-2x(-8 + x) + 4x = -12
(-8 * -2x + x * -2x) + 4x = -12
(16x + -2x2) + 4x = -12

Reorder the terms:
16x + 4x + -2x2 = -12

Combine like terms: 16x + 4x = 20x
20x + -2x2 = -12

Solving
20x + -2x2 = -12

Solving for variable 'x'.

Reorder the terms:
12 + 20x + -2x2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + 20x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 10x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 10x + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + 10x + -1x2 = 0

Solving
6 + 10x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -10x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -10x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -10x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -10x + x2 = 0 + 6
-10x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-10x + x2 = 6

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 6 + 25

Reorder the terms:
25 + -10x + x2 = 6 + 25

Combine like terms: 6 + 25 = 31
25 + -10x + x2 = 31

Factor a perfect square on the left side:
(x + -5)(x + -5) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + -5) equal to 5.567764363 and -5.567764363.

Subproblem 1
x + -5 = 5.567764363

Simplifying
x + -5 = 5.567764363

Reorder the terms:
-5 + x = 5.567764363

Solving
-5 + x = 5.567764363

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.567764363 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.567764363 + 5
x = 5.567764363 + 5

Combine like terms: 5.567764363 + 5 = 10.567764363
x = 10.567764363

Simplifying
x = 10.567764363

Subproblem 2
x + -5 = -5.567764363

Simplifying
x + -5 = -5.567764363

Reorder the terms:
-5 + x = -5.567764363

Solving
-5 + x = -5.567764363

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.567764363 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.567764363 + 5
x = -5.567764363 + 5

Combine like terms: -5.567764363 + 5 = -0.567764363
x = -0.567764363

Simplifying
x = -0.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.567764363, -0.567764363}
Solution
x = {10.567764363, -0.567764363}