The states that if ##ab=0##, then either ##a=0## or ##b=0##.

Example: find the roots of ##x^2-x-6##.

##x^2-x-6=0##

##(x-3)(x+2)=0##

Now, the zero factor property can be applied, since two thing are being multiplied and equal zero.

We know that either

##x-3=0color(white)(ssss)## or ##color(white)(ssss)x+2=0##

Solve both to find that ##x=3## or ##x=-2##.