whenever you find any boolean expression that cannot be solved directly, try to add variables like (1+b),(b+b').....
consider LHS
A'D'+ABC+BCD'
=>A'D'(B+B')+BCD'(A+A')+ABC
=>A'D'B+A'D'B'+ABCD'+A'BCD'+ABC
=>A'D'B(1+C)+A'D'B'+ABC(1+D')
=>A'D'B+A'B'D'+ABC
=>A'D'(B+B')+ABC
=>A'D'+ABC=RHS