a'bc'd+a'bcd+abd=bd
Equations in Boolean algebra represent variables and operations and they follow specific laws and rules. In order to simplify this equation, we can apply these rules and laws. Rule \"a + ab = a\" simplifies the equation to the following form:\n\n- a'bc'd + a'bcd = a'bc'd\n- abd = abd\n\nGiven equation is simplified to a'bc'd + abd = bd.\n\nWe can apply the Consensus theorem which states that (a AND b) OR (NOT a AND c) = (a AND b) OR c for any boolean variables a, b and c. Consequently, we can simplify equation to:\n\na'bc' + bcd + abd = a'c' + ab + bd = bd (equivalent of the consensus theorem)\n\nFinally, we get a simplified equation: bd = bd.