We analyze VLT/X-shooter data for 7 quasars, where we study the relationships between their broad absorption line (BAL) and emission line outflows. We find: 1) the luminosity of the [OIII] $\lambda$5007 emission profile decreases with increasing electron number density (n$_e$) derived from the BAL outflow in the same quasar, 2) the measured velocity widths from the [OIII] emission features and CIV absorption troughs in the same object are similar, and 3) the mean radial velocity derived from the BAL outflow is moderately larger than the one from the [OIII] emission outflow. These findings can be explained by the physical interpretation that the [OIII] and BAL outflow are different manifestations of the same wind. When we have outflows with smaller distances to the central source, their n$_e$ is higher. Therefore, the [OIII] emission is collisionally de-excited and the [OIII] luminosity is then suppressed. Comparisons to previous studies show that the objects in our sample exhibit broad [OIII] emission features similar to the ones in extremely red quasars (ERQs). This might imply that BAL quasars and ERQs have the same geometry of outflows or are at a similar evolutionary stage. We found that the physical parameters derived from the BAL outflows can explain the amount of observed [OIII] luminosity, which strengthens our claim of both BAL and [OIII] outflows are from the same wind. These estimates can be tested with upcoming James Webb Space Telescope observations.