How to find the critical number of the given function:

$\displaystyle f(x)= x^3(x-2)^2 $

Attempt:

$\displaystyle f'(x)=(x^3)(2[x-2][1])+(x-2)^2(3x^2) $

Now we have to equate f'(x) to zero

$\displaystyle f'(x)=(x^3)(2[x-2])+(x-2)^2(3x^2) =0$

After this step I dont know how to simplify to get the x co-ordinates or critical numbers

Please answer in steps.

Thank you