No Wireless on Ubuntu 16.04

I just installed Ubuntu 16.04, and there is no wireless. I don't mean it doesn't work, it seems to be a completely foreign concept to the system. Right-clicking on the network icon shows an Ethernet connection (don't know to what, I guess it's just a dummy connection) but there is no wireless or any option to connect to it.

A couple of forum posts that I googled up about the same problem mention checking one's hardware with lshw. I did, and the Ethernet interface is the only entry listed under "network", there's no mention of wireless.

The "additional drivers" tab under Software & Updates says "no additional drivers found".

Any idea what this could be? Is this just a missing driver?

I'm going to keep looking for solutions myself, but if any of you have some pointers as to what I should be looking for and where, that'd be great. It seems like most of the answers I can find use tools or refer to things that are just not there.

EDIT: So I've tried a couple things suggested on various forums, although I don't really know what most of them mean:

iwconfig ==>

enp3s0 no wireless extensions.

lo no wireless extensions.

modprobe wl ==>

modprobe: FATAL: Module wl not found in directory /lib/modules/4.4.0-21-generic

sudo service network-manager restart ==>

no output, but now all options in the network menu are grayed-out and the (fake)ethernet connection from before is gone.

Turn off secure boot in the BIOS: Already did that, didn't work.

There also is an entry for my wireless card in the output of lshw, maybe I missed it yesterday:

*-network
   description: Network controller
   product: BCM43142 b/g/n
   vendor: Broadcom Corporation
   physical id: 0
   bus info: pci@0000:02:00.0
   version: 01
   width: 64 bits
   clock: 33 MHz
   capabilities: pm msi pciexpress bus_master cap_list
   configuration: driver=bcma-pci-bridge latency=0
   resources: irq:36 memory:f0c00000-f0c07fff

EDIT: Solved! Thanks to u/boomboomsubban, at whose advice I did this:

Try this first, seems to have success

sudo apt-get install ubuntu-restricted-extras

sudo apt-get install bcmwl-kernel-source

You might need to apt-get update between. Reboot, and run

sudo modprobe wl

Which worked, and I'm now editing this from my new laptop on Ubuntu with no cables in my device at all.