0=6x^2-x^3

Solution for 0=6x^2-x^3 equation:

Simplifying
0 = 6x2 + -1x3

Solving
0 = 6x2 + -1x3

Solving for variable 'x'.
Remove the zero:
-6x2 + x3 = 6x2 + -1x3 + -6x2 + x3

Reorder the terms:
-6x2 + x3 = 6x2 + -6x2 + -1x3 + x3

Combine like terms: 6x2 + -6x2 = 0
-6x2 + x3 = 0 + -1x3 + x3
-6x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-6x2 + x3 = 0

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

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 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

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

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