is solve f(x) = 0 for x the same thing as solve f(x) = 0? Would you do the same thing or does the difference in the wording make it a different question?

they are the same. "Solve f(x)=0 for x" is redundant. Since you only have one variable, you can't solve for anything else.

Solve f(x)=0 means to find a value for x which makes f(x) zero.