(0+ 11*0) + (0 +11*0)(1 +01*0)* (1 +01*0) =1*0(1 +01*0)*
Call $(0+11^*0)$ as A and $(1+01^*0)$ as B. Then what you have on left-hand side is just: $$ R = A + AB^*B$$
Using Arden's Theorem we know that in this case: $$R = AB^*$$

Then what we have simplified is: $$(11^*0+0)(1+01^*0)^*$$
Another simplification using Arden's Theorem would give us:
$$(11^*+ \epsilon)0(1+01^*0)^*$$
Which is finally equivalent to: $$1^*0(1+01^*0)^*$$