0=-6x^2+x^3

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

Simplifying
0 = -6x2 + x3

Solving
0 = -6x2 + x3

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

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

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

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

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