0=20x^3-120x^2

Solution for 0=20x^3-120x^2 equation:

Simplifying
0 = 20x3 + -120x2

Reorder the terms:
0 = -120x2 + 20x3

Solving
0 = -120x2 + 20x3

Solving for variable 'x'.
Remove the zero:
120x2 + -20x3 = -120x2 + 20x3 + 120x2 + -20x3

Reorder the terms:
120x2 + -20x3 = -120x2 + 120x2 + 20x3 + -20x3

Combine like terms: -120x2 + 120x2 = 0
120x2 + -20x3 = 0 + 20x3 + -20x3
120x2 + -20x3 = 20x3 + -20x3

Combine like terms: 20x3 + -20x3 = 0
120x2 + -20x3 = 0

Factor out the Greatest Common Factor (GCF), '20x2'.
20x2(6 + -1x) = 0

Ignore the factor 20.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 6}