-8(x+2x)(x-12)=160

Solution for -8(x+2x)(x-12)=160 equation:

Simplifying
-8(x + 2x)(x + -12) = 160

Combine like terms: x + 2x = 3x
-8(3x)(x + -12) = 160

Remove parenthesis around (3x)
-8 * 3x(x + -12) = 160

Reorder the terms:
-8 * 3x(-12 + x) = 160

Multiply -8 * 3
-24x(-12 + x) = 160
(-12 * -24x + x * -24x) = 160
(288x + -24x2) = 160

Solving
288x + -24x2 = 160

Solving for variable 'x'.

Reorder the terms:
-160 + 288x + -24x2 = 160 + -160

Combine like terms: 160 + -160 = 0
-160 + 288x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-20 + 36x + -3x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-20 + 36x + -3x2)' equal to zero and attempt to solve:

Simplifying
-20 + 36x + -3x2 = 0

Solving
-20 + 36x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
6.666666667 + -12x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -12x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -12x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -12x + x2 = 0 + -6.666666667
-12x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-12x + x2 = -6.666666667

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -6.666666667 + 36

Reorder the terms:
36 + -12x + x2 = -6.666666667 + 36

Combine like terms: -6.666666667 + 36 = 29.333333333
36 + -12x + x2 = 29.333333333

Factor a perfect square on the left side:
(x + -6)(x + -6) = 29.333333333

Calculate the square root of the right side: 5.416025603

Break this problem into two subproblems by setting 
(x + -6) equal to 5.416025603 and -5.416025603.

Subproblem 1
x + -6 = 5.416025603

Simplifying
x + -6 = 5.416025603

Reorder the terms:
-6 + x = 5.416025603

Solving
-6 + x = 5.416025603

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 5.416025603 + 6

Combine like terms: -6 + 6 = 0
0 + x = 5.416025603 + 6
x = 5.416025603 + 6

Combine like terms: 5.416025603 + 6 = 11.416025603
x = 11.416025603

Simplifying
x = 11.416025603

Subproblem 2
x + -6 = -5.416025603

Simplifying
x + -6 = -5.416025603

Reorder the terms:
-6 + x = -5.416025603

Solving
-6 + x = -5.416025603

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -5.416025603 + 6

Combine like terms: -6 + 6 = 0
0 + x = -5.416025603 + 6
x = -5.416025603 + 6

Combine like terms: -5.416025603 + 6 = 0.583974397
x = 0.583974397

Simplifying
x = 0.583974397

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.416025603, 0.583974397}
Solution
x = {11.416025603, 0.583974397}