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

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

Simplifying
x3 + 8x2 + 20x = 0

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

Solving
20x + 8x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + 8x + x2) = 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 '(20 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
20 + 8x + x2 = 0

Solving
20 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 8x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + 8x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 8x + x2 = 0 + -20
8x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
8x + x2 = -20

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -20 + 16

Reorder the terms:
16 + 8x + x2 = -20 + 16

Combine like terms: -20 + 16 = -4
16 + 8x + x2 = -4

Factor a perfect square on the left side:
(x + 4)(x + 4) = -4

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}