Question 141580
{{{f(x)=x (x+3)^4(2x+3)^2}}}
Look at each factor individually and set it to zero.
Solve for x. 
Any exponent of the factor becomes its multiplicity.
x=0, multiplicity 1.
(x+3)=0
x=-3, multiplicity 4.
(2x+3)=0
x=-3/2 multiplicity 2.