The E36 mirrors are simply clipped into place. The Bentley manual says to
gently pry the mirrors off with a small screwdriver. There is a plastic
framework hiding behind the glass that the mirror motor moves around when
adjusting the mirror. Your new mirror should have clippy things on the back
that are the same as what is on the broken mirror.
The plastic clips can break if they are very cold. If it's a warm day there
shouldn't be a problem, but if it's cold, gently warming the inside of the
mirror with a hair dryer will reduce the chances considerably.
Wouldn't be a bad idea to warm it anyway as the nylon type plastic used
tends to get more brittle with age in any case.
Give it a few minutes with the hair dryer to give the plastic a chance to
soak up the heat.
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