Please solve step by $$step and do $$all calculations clearly,with plots

Q$1.$Consider the unity negative feedback system with the open$-$loop transfer function given as

G$($s$)=$K$[($s$+10)/($s$($s$+1)($s$+5)($s$+6))]$

a$.$Sketch the root locus for K$0$with all the details like breakaway and breakin points and imaginary axis crossings.

b$.$Show on $$the root locus the point$($s$)$at $$which the closed$-$loop system has poles with real part $-8.$

c$.$Find the value of$$K$0$at $$which the closed loop$-$system has poles with real part $-8.$

d$.$Find all closed$-$loop poles when K$0$is $$adjusted at $$the value found in $$part$-$c$.$

e$.$Based on $$your root locus, find the range of$$K$0$for closed$-$loop stability.