We know that give any pair of real numbers A and B, the following statement will be true:
![A\cdot B=0](https://img.qammunity.org/2023/formulas/mathematics/college/579pdfku23v0f2bs01y46jprnb4cg2csfs.png)
if, and only if
![\begin{gathered} A=0 \\ or \\ B=0 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/6bypuks6qty9qflsfljloog71v3jvt4w8u.png)
Now, if we factor a quadratic equation into two factors A and B, and use the fact we've just mentioned, we can then equal each factor to zero, solve for x and get the solutions to said quadratic equation.