We attempt to find systematically 12-fold quasiperiodic tilings using the substitution method. Only squares, equilateral triangles, and rhombi are considered as tiles. We show that a rosette with these tiles defines directly two different inflation factors. Tilings with these inflation factors are presented. We propose that many more inflation factors could be used and we show that the inflation factor determines the number of triangles used in substitution rules. Different tilings of the same inflation factor can be obtained by exchanging rhombi and squares, thereby changing the position of triangles. Imposing symmetries makes it possible to make an exhaustive search for substitution rules. Thus we obtain many new tilings.