8x^3-24x^2-116x=0

Solution for 8x^3-24x^2-116x=0 equation:

Simplifying
8x3 + -24x2 + -116x = 0

Reorder the terms:
-116x + -24x2 + 8x3 = 0

Solving
-116x + -24x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-29 + -6x + 2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-29 + -6x + 2x2)' equal to zero and attempt to solve:

Simplifying
-29 + -6x + 2x2 = 0

Solving
-29 + -6x + 2x2 = 0

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

Divide each side by '2'.
-14.5 + -3x + x2 = 0

Move the constant term to the right:

Add '14.5' to each side of the equation.
-14.5 + -3x + 14.5 + x2 = 0 + 14.5

Reorder the terms:
-14.5 + 14.5 + -3x + x2 = 0 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + -3x + x2 = 0 + 14.5
-3x + x2 = 0 + 14.5

Combine like terms: 0 + 14.5 = 14.5
-3x + x2 = 14.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 14.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 14.5 + 2.25

Combine like terms: 14.5 + 2.25 = 16.75
2.25 + -3x + x2 = 16.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 16.75

Calculate the square root of the right side: 4.092676386

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.092676386 and -4.092676386.

Subproblem 1
x + -1.5 = 4.092676386

Simplifying
x + -1.5 = 4.092676386

Reorder the terms:
-1.5 + x = 4.092676386

Solving
-1.5 + x = 4.092676386

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 4.092676386 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.092676386 + 1.5
x = 4.092676386 + 1.5

Combine like terms: 4.092676386 + 1.5 = 5.592676386
x = 5.592676386

Simplifying
x = 5.592676386

Subproblem 2
x + -1.5 = -4.092676386

Simplifying
x + -1.5 = -4.092676386

Reorder the terms:
-1.5 + x = -4.092676386

Solving
-1.5 + x = -4.092676386

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -4.092676386 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.092676386 + 1.5
x = -4.092676386 + 1.5

Combine like terms: -4.092676386 + 1.5 = -2.592676386
x = -2.592676386

Simplifying
x = -2.592676386

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.592676386, -2.592676386}
Solution
x = {0, 5.592676386, -2.592676386}