A multiplication is zero if and only if at least one of the factors is zero. So, in this case, the multipications equals zero when
[tex] x^2+4 = 0 \quad \lor \quad x-3=0 [/tex]
The first equation has no real solutions, because [tex] x^2 [/tex] is a square, and thus it's positive. If you add 4 to a positive number, the result can't be zero.
The second equation has the solution
[tex] x-3=0 \iff x=3 [/tex]
So, globally, the expression equals zero if and only if [tex] x=3 [/tex]
