The trick I use to keep all the units straight is I memorize how they are related to each other. It doesn't sound like it would work, but let me explain.
For example, F = m x a is the second law. You know that acceleration is meters per second squared, and you know that force is Newtons. A Newton is 1 kilogram x 9.8 meters per second squared (1 gravity). Knowing this, you can solve for the units of mass.
In mechanical physics, every unit can be stated in terms of the meter, the second or the kilogram. That's the way they are designed. So if you just remember how each unit relates to the basic units of measurement, you can generally figure everything out. I actually never memorized Newton's Second Law. I just knew that it had something to do with mass, force and acceleration, so I put together an equation where all the units cancel out.
It sounds complicated, and maybe it won't work for you. But it worked for me, so I thought it might be worth a try.
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