Task B-2.1. Determine all solutions of the equation $(x+1)^{2}(x-4)^{2}+4\left(x^{2}-3 x-4\right)=0$.
## Solution.

We can write the given equation in the form

$$
\left(x^{2}-3 x-4\right)^{2}+4\left(x^{2}-3 x-4\right)=0
$$

If we factor out the common factor on the left side of the equation, we get

$$
\left(x^{2}-3 x-4\right)\left(x^{2}-3 x-4+4\right)=0
$$

or

$$
\begin{aligned}
& \left(x^{2}-3 x-4\right)\left(x^{2}-3 x\right)=0 \\
& (x+1)(x-4) x(x-3)=0
\end{aligned}
$$

The solutions to the given equation are $-1,0,3,4$.

(1 point)