0=-8(3x^2-36x-128)

Solution for 0=-8(3x^2-36x-128) equation:

Simplifying
0 = -8(3x2 + -36x + -128)

Reorder the terms:
0 = -8(-128 + -36x + 3x2)
0 = (-128 * -8 + -36x * -8 + 3x2 * -8)
0 = (1024 + 288x + -24x2)

Solving
0 = 1024 + 288x + -24x2

Solving for variable 'x'.

Combine like terms: 0 + -1024 = -1024
-1024 + -288x + 24x2 = 1024 + 288x + -24x2 + -1024 + -288x + 24x2

Reorder the terms:
-1024 + -288x + 24x2 = 1024 + -1024 + 288x + -288x + -24x2 + 24x2

Combine like terms: 1024 + -1024 = 0
-1024 + -288x + 24x2 = 0 + 288x + -288x + -24x2 + 24x2
-1024 + -288x + 24x2 = 288x + -288x + -24x2 + 24x2

Combine like terms: 288x + -288x = 0
-1024 + -288x + 24x2 = 0 + -24x2 + 24x2
-1024 + -288x + 24x2 = -24x2 + 24x2

Combine like terms: -24x2 + 24x2 = 0
-1024 + -288x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-128 + -36x + 3x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-128 + -36x + 3x2)' equal to zero and attempt to solve:

Simplifying
-128 + -36x + 3x2 = 0

Solving
-128 + -36x + 3x2 = 0

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

Divide each side by '3'.
-42.66666667 + -12x + x2 = 0

Move the constant term to the right:

Add '42.66666667' to each side of the equation.
-42.66666667 + -12x + 42.66666667 + x2 = 0 + 42.66666667

Reorder the terms:
-42.66666667 + 42.66666667 + -12x + x2 = 0 + 42.66666667

Combine like terms: -42.66666667 + 42.66666667 = 0.00000000
0.00000000 + -12x + x2 = 0 + 42.66666667
-12x + x2 = 0 + 42.66666667

Combine like terms: 0 + 42.66666667 = 42.66666667
-12x + x2 = 42.66666667

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 = 42.66666667 + 36

Reorder the terms:
36 + -12x + x2 = 42.66666667 + 36

Combine like terms: 42.66666667 + 36 = 78.66666667
36 + -12x + x2 = 78.66666667

Factor a perfect square on the left side:
(x + -6)(x + -6) = 78.66666667

Calculate the square root of the right side: 8.869423131

Break this problem into two subproblems by setting 
(x + -6) equal to 8.869423131 and -8.869423131.

Subproblem 1
x + -6 = 8.869423131

Simplifying
x + -6 = 8.869423131

Reorder the terms:
-6 + x = 8.869423131

Solving
-6 + x = 8.869423131

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 = 8.869423131 + 6

Combine like terms: -6 + 6 = 0
0 + x = 8.869423131 + 6
x = 8.869423131 + 6

Combine like terms: 8.869423131 + 6 = 14.869423131
x = 14.869423131

Simplifying
x = 14.869423131

Subproblem 2
x + -6 = -8.869423131

Simplifying
x + -6 = -8.869423131

Reorder the terms:
-6 + x = -8.869423131

Solving
-6 + x = -8.869423131

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 = -8.869423131 + 6

Combine like terms: -6 + 6 = 0
0 + x = -8.869423131 + 6
x = -8.869423131 + 6

Combine like terms: -8.869423131 + 6 = -2.869423131
x = -2.869423131

Simplifying
x = -2.869423131

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.869423131, -2.869423131}
Solution
x = {14.869423131, -2.869423131}