How do I solve this:

5a^2(3a+4)(a+2)(a^2+25)

please help and thank you

So far, there's nothing to solve. If you want to solve

5a^2(3a+4)(a+2)(a^2+25) = 0

then a product is zero if any of its factors is zero.
To wit,
5 -- never zero
a^2 -- zero if a=0
3a+4 -- zero if a = -4/3
a+2 -- zero if a = -2
a^2+25 -- never zero, since a^2>=0 and a^2+25 >= 25