-2x(x-8)=20

Solution for -2x(x-8)=20 equation:

Simplifying
-2x(x + -8) = 20

Reorder the terms:
-2x(-8 + x) = 20
(-8 * -2x + x * -2x) = 20
(16x + -2x2) = 20

Solving
16x + -2x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 16x + -2x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 8x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
-10 + 8x + -1x2 = 0

Solving
-10 + 8x + -1x2 = 0

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

Divide each side by '-1'.
10 + -8x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -8x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -8x + x2 = 0 + -10

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

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

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 = -10 + 16

Reorder the terms:
16 + -8x + x2 = -10 + 16

Combine like terms: -10 + 16 = 6
16 + -8x + x2 = 6

Factor a perfect square on the left side:
(x + -4)(x + -4) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -4) equal to 2.449489743 and -2.449489743.

Subproblem 1
x + -4 = 2.449489743

Simplifying
x + -4 = 2.449489743

Reorder the terms:
-4 + x = 2.449489743

Solving
-4 + x = 2.449489743

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 = 2.449489743 + 4

Combine like terms: -4 + 4 = 0
0 + x = 2.449489743 + 4
x = 2.449489743 + 4

Combine like terms: 2.449489743 + 4 = 6.449489743
x = 6.449489743

Simplifying
x = 6.449489743

Subproblem 2
x + -4 = -2.449489743

Simplifying
x + -4 = -2.449489743

Reorder the terms:
-4 + x = -2.449489743

Solving
-4 + x = -2.449489743

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 = -2.449489743 + 4

Combine like terms: -4 + 4 = 0
0 + x = -2.449489743 + 4
x = -2.449489743 + 4

Combine like terms: -2.449489743 + 4 = 1.550510257
x = 1.550510257

Simplifying
x = 1.550510257

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.449489743, 1.550510257}
Solution
x = {6.449489743, 1.550510257}