Find roots of following polynomial and find zeroes of multiplicity.

f(x) = 4x^5 + 12x^4 + 9x^3

I got:

f(x) = 4x^5 + 12x^4 + 9x^3 = 0

x^3(4x^2 + 12x + 9) = 0

x^3(2x + 3)(2x + 3) = 0

x=0 OR x= -3/2

Because (2x+3) occurs two times, the multiplicity of -3/2 is 2 and the multiplicity of 0 is 1

Is it correct? Does it fully answer the question?