Solve[(u-(1/p)*Y)*F[p]==Y,Y]

Y/.Solve[((((u-Y)/(p+2))-u-Y)/(p-3))==Y,Y][[1]]//Simplify

Solve[3-(p^2)==0.]

Y/.Solve[((((Y-u)/p)-((Y-u)/(p+2)))/(p+1))==Y,Y][[1]]//Simplify

Denominator[%]==0.//Solve

Eigenvalues[(({{1, 1}, {-2, 4}}))]

Solve[{p*x1==-u+x1+x2,p*x2==3u-2x1+4x2},x2,x1]

Solve[6-5 p+(p^2)==0]