I just had a basic question if your given an equation = 0 in Z29 you can just factor and solve because 29 in prime right? if 29 isnt prime then you would have to check all solutions?
Yep. A polynomial $\displaystyle f$ with coefficients in $\displaystyle \mathbb{Z}/p\mathbb{Z}$ has at most deg(f) zero's in $\displaystyle \mathbb{Z}/p\mathbb{Z}$