Question: I have tried to solve the following equation:

$$
(z+1)^4+4(z-1)^4=0 \quad,\quad z=(a+bi)
$$

If I could leave the $z^4$ alone I could solve it using the formula, but I do not know how to operate with it having additions and substractions. 

Can someone please help me?
Thank you!

Answer: 
$$(z+1)^4 +4(z-1)^4=0$$
$$\Rightarrow \Big(\frac{z+1}{z-1} \Big)^4=-4$$
$$\Rightarrow \frac{z+1}{z-1}=\alpha$$
Where $\alpha$ respresent all four roots of $x^4 +4=0$
hence 
$$\Rightarrow \frac{z}{1}= \frac{\alpha+1}{\alpha-1}$$
What would you do if you had
$$
(z+1)^4-4(z-1)^4=0
$$
instead? You'd observe it is
$$
((z+1)^2-2(z-1)^2)((z+1)^2+2(z-1)^2)=0
$$
Well, with $+$ you can write it as
$$
(z+1)^4-(2i)^2(z-1)^4=0
$$