algebra

1) expand
2) rearrange the pairs, put the ones with squares first
3) the first 2 factorise as a difference of two squares,
4) the second two factorise so that one of the factors is the same as one of the part 3 factors
5) take out the common factor so that it is now factoised properly.
6)since the answer is 0, one of the factors must be 0
This is enough hints for now, your turn

If this is not enough information ask for more but have a go yourself first.

a(a-x) + 4b(x-4b) = 0
a^2 - ax + 4bx - (4b)^2 = 0
a^2 -ax + 4bx - 16b^2 = 0
-ax + 4bx = -a^2 + 16b^2
x(-a + 4b) = a^2 + 16b^2
x = (a^2 + 16b^2) / (-a + 4b)

Ok
Our guest has made a careless mistake leaving out a minus sign on the second last row (and last row). Other than that trivial error, the maths is good.
It is slightly different from my method but it is still good.
It is not quite finished.
If you fix up the minus sign then there is a difference of 2 squares on the top that can be factorised,
then there is some cancelling that can be done and the final answer is much simpler.

Did anyone get a final solution for this?