We analyse the broad-range shape of the monopole and quadrupole correlation functions of 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 $f(z)sigma_8(z)$, and the physical matter density $Omega_mh^2$. 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. However, such Monte Carlo Markov Chain analysis is computationally expensive for advanced theoretical models, thus we develop a new methodology to speed up our analysis. We obtain ${D_A(z)r_{s,fid}/r_s$Mpc, $H(z)r_s/r_{s,fid}$kms$^{-1}$Mpc$^{-1}$, $f(z)sigma_8(z)$, $Omega_m h^2}$ = ${956pm28$ , $75.0pm4.0$ , $0.397 pm 0.073$, $0.143pm0.017}$ at $z=0.32$ and ${1421pm23$, $96.7pm2.7$ , $0.497 pm 0.058$, $0.137pm0.015}$ at $z=0.59$ where $r_s$ is the comoving sound horizon at the drag epoch and $r_{s,fid}=147.66$Mpc for the fiducial cosmology in this study. In addition, we divide the galaxy sample into four redshift bins 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 $Omega_m=0.306pm0.009$, $H_0=67.9pm0.7$kms$^{-1}$Mpc$^{-1}$, and $sigma_8=0.815pm0.009$ assuming $Lambda$CDM; $Omega_k=0.000pm0.003$ assuming oCDM; $w=-1.01pm0.06$ assuming $w$CDM; and $w_0=-0.95pm0.22$ and $w_a=-0.22pm0.63$ assuming $w_0w_a$CDM. Our results show no tension with the flat $Lambda$CDM cosmological paradigm. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS.
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