In the following equation, determine $p$ so that -1 is one of the roots of the equation:

$$
(2 p-1) x^{2}+2(1-p) x+3 p=0
$$
Ha -1 is a root of the equation, then

$$
\begin{gathered}
(2 p-1)\left(-1^{2}\right)+2(1-p)(-1)+3 p=0 \\
7 p=3
\end{gathered}
$$

or

$$
p=\frac{3}{7}
$$

(Andor Vilcsek, Eger.)

The problem was also solved by: Bauer E., Csada I., Dénes M., Ehrenfeld N., Erdős V., Felhőssy J., Fried E., Füstös P., Grün K., Kirchknopf E., Kürth R., Lengyel P., Lusztig M., Neumann F., Paunz A., Rosenthal M., Sárközy P., Spitzer L., Szóke D., Tóth B., Wáhl V.