The mirror in my restroom has got spots on it.
I tried washing it with soap and shampoo however they don't go away.
How can I get this mirror to shine again ?
It looks like it is scale, which is build up chalk. As with all scale, vinegar and lemon juice, among other things, will get rid of it.
Best option might be cleaning strength vinegar but all different kinds of vinegar as well as many kinds of lemon and lime juice will clean scale. I expect there are commercially made cleaners that will do the job, based on other accids as well as those I mention.
For as strong build up as this I would use a bit of undiluted vinegar or lemon juice on a bit of cloth or paper and just rub it on, wash it off after with plenty of water.
When using a commercial cleaner, follow instructions on the packaging. Some might be so much stronger that gloves are needed.
If it was clear glass I would submerge it in a vinegar solution, but some mirror backings, some glues and some frame materials will not do well in that.
To avoid a new build up, clean off your mirror after every use in which it gets wet. If the water where you live is hard (contains a lot of chalk) it might be needed to use a wipe with a bit of vinegar or lemon juice.
A lifehack to avoid water staying on the mirror is to wipe it with a little soap. Just a tiny bit, and wipe it off with a dry cloth or piece of paper.
This can be any kind of soap and it has to be a very little bit. Just drag a wet finger over a block of soap and use that little, or use the bit of liquid soap that is still on the dispenser after using it.
The best possible thing you can do is go to your nearest grocery store and grab a bottle of windex! It's esspecially made for windows and mirror are extremely similar to mirrors. This is what i use and it leaves my mirrors spotless! Use this with either a paper towel or a clean towel and it will do the trick!