solve a quadratic as a by-product of any work you do for the equations of this semester (usually factoring, if you cannot factor it, by the quadratic formula)
factor a polynomial by grouping to solve its equation
Given a polynomial and a factor, use division to find all of the zeros.
solve a square root equation by squaring both sides
solve exponentials with a common base for an exact answer, or with log to get a rounded answer
solve logarithmic equation using properties of logarithm
factor to find a common denominator to use to solve rational equations (and reject answers when appropriate)