((1/(s(((s+1))^2)))/(1+K(1/(s(((s+1))^2))))) //Simplify

Manipulate[
{NyquistPlot[K(1/(s(((s+1))^2))) /.K->KK,PlotRange->{{-2,0.5},{-2,2}}],
Solve[K+s (((1+s))^2)==0 /.K->KK,s]},{KK,0.5,3}]