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

Simplify[Y[p]/.Solve[((((u-Y[p])/(p+2))+u-Y[p])/(p+1))==Y[p],Y[p]][[1]]]
Solve[Denominator[((%)/u)]==0]

Simplify[Y[p]/.Solve[(((u-Y[p])/(p+2))-((u-Y[p])/(p+1)))(1/p)==Y[p],Y[p]][[1]]]
Solve[Denominator[((%)/u)]==0.]

Eigenvalues[(({{-1, 1}, {3, 2}}))]//N

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

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