$\sin(x + 30°).\cos(x - 45°) = 0$
$\Rightarrow \left\{ \begin{array}{l} \sin(x+30^o)=0 (1)\\ \cos(x-45^o)=0(2) \end{array} \right .$
$(1)\Rightarrow x+30^o=k180^o\Rightarrow x=-30^o+k180^o(k\in\mathbb Z)$
$(2)\Rightarrow x-45^o=k180^o\Rightarrow x=45^o+k180^o(k\in\mathbb Z)$