8x^3+16x^2+20x+0=0

Solution for 8x^3+16x^2+20x+0=0 equation:

Simplifying
8x3 + 16x2 + 20x + 0 = 0

Reorder the terms:
0 + 20x + 16x2 + 8x3 = 0
Remove the zero:
20x + 16x2 + 8x3 = 0

Solving
20x + 16x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(5 + 4x + 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 '(5 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + 4x + 2x2 = 0

Solving
5 + 4x + 2x2 = 0

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

Divide each side by '2'.
2.5 + 2x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 2x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 2x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 2x + x2 = 0 + -2.5
2x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
2x + x2 = -2.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -2.5 + 1

Reorder the terms:
1 + 2x + x2 = -2.5 + 1

Combine like terms: -2.5 + 1 = -1.5
1 + 2x + x2 = -1.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = -1.5

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}