8x^3+x^2+8x=0

Solution for 8x^3+x^2+8x=0 equation:

Simplifying
8x3 + x2 + 8x = 0

Reorder the terms:
8x + x2 + 8x3 = 0

Solving
8x + x2 + 8x3 = 0

Solving for variable 'x'.

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

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 '(8 + x + 8x2)' equal to zero and attempt to solve:

Simplifying
8 + x + 8x2 = 0

Solving
8 + x + 8x2 = 0

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

Divide each side by '8'.
1 + 0.125x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.125x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 0.125x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.125x + x2 = 0 + -1
0.125x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.125x + x2 = -1

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.125x + 0.25 + x2 = -1 + 0.25

Reorder the terms:
0.25 + 0.125x + x2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + 0.125x + x2 = -0.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}