Find describes the successful outcome of a search or a discovery.
Our company hopes to find oil off the coast of Mexico.
Alexander Fleming found a mold growing in
his bacteria culture.
Find out describes a change in knowledge that the subject has about the world. First the subject is unaware of the fact; then the subject becomes aware of the fact.
We found out why the pipes were corroding so quickly.
Know describes the information that the subject has available at any given time. Know is a state verb and does not appear in the progressive.
We knew that there was little chance of success, but we tried the experiment anyway.
She is knowing three chemicals that will
serve our purposes.
She knows three chemicals that will serve