We analyse the broad-range shape of the monopole and quadrupole correlation functions of 2 Chuang et al.the BOSS Data Release 12 (DR12) CMASS and LOWZ galaxy sample to obtain constraints on the Hubble expansion rate H(z), the angular-diameter distance D A (z), the normalised growth rate f (z)σ 8 (z), and the physical matter density Ω m h 2 . We adopt wide and flat priors on all model parameters in order to ensure the results are those of a 'single-probe' galaxy clustering analysis. We also marginalise over three nuisance terms that account for potential observational systematics affecting the measured monopole. The Monte Carlo Markov Chain analysis with such wide priors and additional polynomial functions is computationally expensive for advanced theoretical models. We develop a new methodology to speed up by scanning the parameter space using a fast model first and then applying importance sampling using a slower but more accurate model.Our measurements for DR12 galaxy sample, using the range, Ω m h 2 } = {956 ± 28 Mpc, 75.0 ± 4.0 km s −1 Mpc −1 , 0.397 ± 0.073, 0.143 ± 0.017} at z = 0.32 and {1421 ± 23 Mpc, 96.7 ± 2.7 km s −1 Mpc −1 , 0.497 ± 0.058, 0.137 ± 0.015} at z = 0.59 where r s is the comoving sound horizon at the drag epoch and r s,f id = 147.66 Mpc is the sound scale of the fiducial cosmology used in this study.In addition, we divide each sample (CMASS and LOWZ) into two redshift bins (four bins in total) to increase the sensitivity of redshift evolution. However, we do not find improvements in terms of constraining dark energy model parameters. Combining our measurements with Planck data, we obtain Ω m = 0.306 ± 0.009, H 0 = 67.9 ± 0.7 km s −1 Mpc −1 , and σ 8 = 0.815 ± 0.009 assuming ΛCDM; Ω k = 0.000 ± 0.003 assuming oCDM; w = −1.01 ± 0.06 assuming wCDM; and w 0 = −0.95 ± 0.22 and w a = −0.22 ± 0.63 assuming w 0 w a CDM. Our results show no tension with the flat ΛCDM cosmological paradigm. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS.