For real and complex numbers, and more generally for elements of an integral domain, a product equals to zero if and only if at least one of the factors equals to zero. For two elements $a$ and $b$ , we have $$ab = 0 \quad \Leftrightarrow \quad a = 0 \, \lor \, b = 0. $$

For example, this rule can be used in solving polynomial equations: $$x^3-x^2-2x+2 = 0$$ $$(x^3-x^2)+(-2x+2) = 0$$ $$x^2(x-1)-2(x-1) = 0$$ $$(x-1)(x^2-2) = 0$$ $$x-1 = 0 \,\lor\, x^2-2 = 0$$ $$x = 1 \,\lor\, x = \pm\sqrt{2}$$

The used sign ``$\lor$ '' is the logical or.