When solving an equation with the Zero Product Property, the first step is factoring the polynomial. Then, each factor is set equal to $0$ and solved as its own equation. $\begin{gathered} x^3-5x^2+7x-3=0\\ \Downarrow \\ (x-3)(x-1)(x-1)=0\\ \Downarrow \\ x-3=0\\ x-1=0\\ x-1=0 \end{gathered}$ In this case, even though there are three factors, solving them will result in only two unique zeros: $x=3$ and $x=1.$ This occurrence is described as the multiplicity of zeros; in the example equation above, the zero $x=3$ has multiplicity $1$ because it only occurs once. On the other hand, $x=1$ has multiplicity $2$ because there are two $(x-1)$ factors.

Note: The multiplicity of a zero being greater than $1$ implies that, algebraically, the zero occurs multiple times. The graph, however, does not intercept the $x\text{-}$axis at this point multiple times. In this example, the zero $x=1$ has a multiplicity of $2$ but the graph intercepts the $x\text{-}$axis at $x=1$ only once.