0=-3x^3+6x^2

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

Simplifying
0 = -3x3 + 6x2

Reorder the terms:
0 = 6x2 + -3x3

Solving
0 = 6x2 + -3x3

Solving for variable 'x'.
Remove the zero:
-6x2 + 3x3 = 6x2 + -3x3 + -6x2 + 3x3

Reorder the terms:
-6x2 + 3x3 = 6x2 + -6x2 + -3x3 + 3x3

Combine like terms: 6x2 + -6x2 = 0
-6x2 + 3x3 = 0 + -3x3 + 3x3
-6x2 + 3x3 = -3x3 + 3x3

Combine like terms: -3x3 + 3x3 = 0
-6x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-2 + x) = 0

Ignore the factor 3.
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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Solution
x = {0, 2}