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 $$ab \;=\; 0 \quad \Longleftrightarrow \quad a \,=\, 0\; \lor \;b \,=\, 0. $$

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.