We have the equation:
![(z-2)(z-1)=0](https://img.qammunity.org/2023/formulas/mathematics/college/57ha4ille1c0ks9cyljnprmhlbxjnitsg1.png)
There are a total of two options that complies the equation, as it is a product.
If the first term is 0, the equation is right.
But if the second term is 0, the equation is right too.
Then both are solutions.
So we have:
![z-2=0](https://img.qammunity.org/2023/formulas/mathematics/college/msq9qe9uwk83h86oq60ff3ynv5pbusd6fq.png)
![z=2](https://img.qammunity.org/2023/formulas/mathematics/college/mdjgoxumhrgzuh91siff7j59upkitqu2cl.png)
And,
![z-1=0](https://img.qammunity.org/2023/formulas/mathematics/college/f58598ysgoqa22hqwxg90wqahkwxs361n8.png)
![z=1](https://img.qammunity.org/2023/formulas/mathematics/college/qv199bxnq91oqqcyb3rnfy3t87ndj3ovyl.png)
Then we can conclude:
The two correct answers are z=2 and z=1
z=1,2 in the format asked.