set the equation equal to 0 and solve for the roots.
x * (3x^2 - 9x + 12) = 0
factor out a 3 to get:
3 * x * (x^2 - 3x + 4) = 0
x^2 - 3x + 4 cannot be factored because the roots are not real.
here's a graph of x^2 - 3x + 4
you can see that it doesn't cross the x-axis so it's roots are not real.
each one of the factors can be set equal to 0.
3*x = 0 yields x = 0
you have a solution at x = 0.
your equation of:
3x^3 - 9x^2 + 12x = 0 becomes 0 when x = 0.
If you make the equation equal to:
y = 3x^3 - 9x^2 + 12x, then you will have a value for y whenever x is a real number which it will always be because there are no restrictions on the domain of this equaion.
a graph of this equation looks like this:
I can't think of anything else to do with this equation.