20x^3+50x^2+60x=0

Solution for 20x^3+50x^2+60x=0 equation:

Simplifying
20x3 + 50x2 + 60x = 0

Reorder the terms:
60x + 50x2 + 20x3 = 0

Solving
60x + 50x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10x'.
10x(6 + 5x + 2x2) = 0

Ignore the factor 10.
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 '(6 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
6 + 5x + 2x2 = 0

Solving
6 + 5x + 2x2 = 0

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

Divide each side by '2'.
3 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 2.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2.5x + x2 = 0 + -3
2.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
2.5x + x2 = -3

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -3 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -3 + 1.5625

Combine like terms: -3 + 1.5625 = -1.4375
1.5625 + 2.5x + x2 = -1.4375

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = -1.4375

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}