1. (x - 4)^5 - 9(x - 4)^3 = 0

find all real solutions for x

2. To visualize this better, let $u = x - 4$.

So our equation becomes: $u^5 - 9u^3 = 0$

Factor out $u^3$ to get: $u^3 (u^2 - 9) = 0$

And notice that the second factor is a difference of squares. Can you carry on from here?