To the power 2001!

$\begin{aligned} 2x^{2001}+3x^{2000}+2x^{1999}+3x^{1998}+\cdots+2x+3 & = 0 \\ (2x+3) (x^{2000}+x^{1998}+x^{1996}+x^{1994} + \cdots+1) & = 0 \\ \implies x & = - \frac 32 \quad \quad \small \color{#3D99F6}{\text{Note that }x^{2000}+x^{1998}+x^{1996}+ \cdots+1 > 0 \text{ has no real root}} \\ & = \boxed{-1.5} \end{aligned}$

We could also use vieta..note that for an n degree polynomial, sum of the zeroes of that polynomial is simply -coefficient of (n-1)th degree term/coefficient of nth degree term..thus this simply comes out to be $\frac {-3}{2}$