how do you clean clogged sinks and drainage?

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this morning while right after my coffee i went to the bathroom to do my morning rituals and to my shock the drainage and sink has clogged and the water hasn't subside. i decided to clean it first before taking my shower but i find it hard to unclog those sinks and drainage, i suspect that it has something to do with my niece and nephew playing in the shower when they take a bath. perhaps they put something in the drainage which cause it to clog. now my problem is how to remove whatever that thing is. i already use a plunger yet it doesn't work. I'm thinking of putting a liquid Sosa but i am not sure if it will work and if it is safe to the drainage. any suggestion guys?