1. **State the problem:** Solve the equation $ (x + 1)(x - 1) = 0 $ for $ x $. 2. **Formula and rule:** The zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. That is, if $ab=0$, then $a=0$ or $b=0$. 3. **Apply the zero product property:** Set each factor equal to zero: $$ x + 1 = 0 $$ $$ x - 1 = 0 $$ 4. **Solve each equation:** For $x + 1 = 0$: $$ x = -1 $$ For $x - 1 = 0$: $$ x = 1 $$ 5. **Final answer:** The solutions to the equation are $x = -1$ and $x = 1$.