-2x(x-8)24=-8

Solution for -2x(x-8)24=-8 equation:

Simplifying
-2x(x + -8) * 24 = -8

Reorder the terms:
-2x(-8 + x) * 24 = -8

Reorder the terms for easier multiplication:
-2 * 24x(-8 + x) = -8

Multiply -2 * 24
-48x(-8 + x) = -8
(-8 * -48x + x * -48x) = -8
(384x + -48x2) = -8

Solving
384x + -48x2 = -8

Solving for variable 'x'.

Reorder the terms:
8 + 384x + -48x2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 384x + -48x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + 48x + -6x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(1 + 48x + -6x2)' equal to zero and attempt to solve:

Simplifying
1 + 48x + -6x2 = 0

Solving
1 + 48x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.1666666667 + -8x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -8x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -8x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -8x + x2 = 0 + 0.1666666667
-8x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-8x + x2 = 0.1666666667

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 0.1666666667 + 16

Reorder the terms:
16 + -8x + x2 = 0.1666666667 + 16

Combine like terms: 0.1666666667 + 16 = 16.1666666667
16 + -8x + x2 = 16.1666666667

Factor a perfect square on the left side:
(x + -4)(x + -4) = 16.1666666667

Calculate the square root of the right side: 4.020779361

Break this problem into two subproblems by setting 
(x + -4) equal to 4.020779361 and -4.020779361.

Subproblem 1
x + -4 = 4.020779361

Simplifying
x + -4 = 4.020779361

Reorder the terms:
-4 + x = 4.020779361

Solving
-4 + x = 4.020779361

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.020779361 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.020779361 + 4
x = 4.020779361 + 4

Combine like terms: 4.020779361 + 4 = 8.020779361
x = 8.020779361

Simplifying
x = 8.020779361

Subproblem 2
x + -4 = -4.020779361

Simplifying
x + -4 = -4.020779361

Reorder the terms:
-4 + x = -4.020779361

Solving
-4 + x = -4.020779361

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.020779361 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.020779361 + 4
x = -4.020779361 + 4

Combine like terms: -4.020779361 + 4 = -0.020779361
x = -0.020779361

Simplifying
x = -0.020779361

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.020779361, -0.020779361}
Solution
x = {8.020779361, -0.020779361}