8. Given that $x_{1}$ and $x_{2}$ are distinct complex numbers, and satisfy the following three equations:
$$
\begin{array}{l}
x_{1}\left(x_{1}+1\right)=A, x_{2}\left(x_{2}+1\right)=A, \\
x_{1}^{4}+3 x_{1}^{3}+5 x_{1}=x_{2}^{4}+3 x_{2}^{3}+5 x_{2} .
\end{array}
$$

Then the value of $A$ that satisfies the above three equations is
$\qquad$
8. -7 .

Applying division we get
$$
\begin{array}{l} 
x_{1}^{4}+3 x_{1}^{3}+5 x_{1} \\
=\left(x_{1}^{2}+x_{1}-A\right)\left(x_{1}^{2}+2 x_{1}+(A-2\right. \\
(A+7) x_{1}+A(A-2) \\
=(A+7) x_{1}+A(A-2) . \\
\text { By } x_{1}^{4}+3 x_{1}^{3}+5 x_{1}=x_{2}^{4}+3 x_{2}^{3}+5 x_{2} \\
\Rightarrow(A+7) x_{1}=(A+7) x_{2} \\
\Rightarrow A=-7 .
\end{array}
$$