Right here goes:
mother = child +21
The mother is 21 years older than the child.
child + 6 = (mother + 6) / 5
In 6 years, the child and the mother are 6 years older and their ages are a factor 5 apart.
So "mother" can be replaced by "child+21) That gives:
child + 6 = (child + 21 + 6) / 5
So
child + 6 = (child