X1=K1*(1-c)(1-d)(1-g/q)(1-g*K)(1-h/q)(1-h*K)+
K2*(1-c)(1-d)(1-g/q)(1-g)(1-h*K)(1-h*K/q)+
K3*(1-c)(1-d)(1-h/q)(1-h)(1-g*K)(1-g*K/q)+
K4*(1-c*K)(1-d*K)(1-g/q)(1-h/q)(1-g)(1-h);
X1=Table[Coefficient[X1,K,i]==0, {i,0,2}];
X1=Solve[X1,{K1,K2,K3,K4}];
X1={K1->Factor[K1/.X1[[1]]],K2->Factor[K2/.X1[[1]]],K3->Factor[K3/.X1[[1]]],K4->Factor[K4/.X1[[1]]]}

{K1->Factor[X1[[1,2]]/X1[[4,2]]],K2->Factor[X1[[2,2]]/X1[[4,2]]],K3->Factor[X1[[3,2]]/X1[[4,2]]],K4->Factor[X1[[4,2]]/X1[[4,2]]]}