Different plastic parts of laptop cases, especially hinges, tend to crack very easily under small amounts of stress. So, it is important to be able to repair these cracks, and prevent them from spreading. After repair, however, it is also important to be gentle with the case, and prevent case damage from occurring again.
Open or close the laptop computer fully so the damage easily accessible.
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Clean out the cracks with a can of dust cleaning air. Do a thorough job of this, as the repair wont last if the surfaces are still dirty.
For small cracks, press the plastic together as close as possible, and fill the crack with standard superglue. Count to 100 before releasing the plastic, and allow the glue to dry for several minutes before moving the case.
For large cracks, place a flat tip on a soldering iron, and plug the iron into a wall outlet. After the soldering iron has heated up, gently melt the plastic on both sides of the crack together. Make sure that the plastic melts deeply, and becomes quite heated. This will allow the plastic to bind together.