Can you get out of the deal if you have already signed an unconditional Agreement of Purchase and Sale?

The Agreement of Purchase and Sale is a legally binding document and is enforceable by the courts.  The only way out of an agreement of purchase and sale is to employ a condition that is crafted into the agreement to protect you.  But if the agreement is unconditional then the only way out of it is if the other party chooses to let you out of the contract.