I installed Vine Linux 6.5 on my laptop lenovo G550 due to the end of support for Windows 7, but I can't connect to the wireless LAN. I didn't have much information, so I'll post a solution.
Go to System> Settings> Internet & Networks> Network Connections, select Wireless and press the Add button. Select the SSID on the Wireless tab and the encryption method (WPA & WPA2 Personal in our case) on the Wireless Security tab, and enter the password. Finally, press the save button to complete the wireless settings. But it doesn't connect. It seems that the built-in wireless LAN adapter is not recognized.
At the terminal
When you type
Network controller: Broadcom Corporation BCM4312 802.11b/g LP-PHY
Came out. The device seems to be recognized.
Then it seems that you need to install the driver for BCM4312.
There is no choice but to connect to the Internet by wire.
Start the synaptic package manager and try searching for it with the name broadcom. I found those drivers.
It seems that it is in the form of building and installing by yourself, probably because of copyright.
After installing it, I was able to connect to the wireless LAN safely.