The P45 has no line outputs, only a stereo headphone output, and when a jack is plugged into the socket the internal speakers are shut off. This is fine for when you're actually using headphones, but if you're recording, or connecting to mixing equipment to play at a gig, you may want the internal speakers to stay working (I did) if you didn't have any external foldback amplifier to use at the same time. There's a few ways you can go about this.
(1) A simple approach is to override the mute-switch in the headphone socket. On mine, if you remove the audio board you can see the headphone socket pins on the underside of the board. The single pin nearest the jack hole is the ground. Next in is 4 pins in a row, with two joined together in the middle, this is the mute switching. And the remaining two pins are the left and right audio signals.
You can permanently bridge all those middle four pins together, so the speakers never shut off. Or, you can wire a SPST switch between the middle two and either of the outer pins, so you get the original speaker muting feature, or not, as you wish. There's just enough space between the headphone and power sockets to fit a switch.
(2) An alternative approach is to leave the headphone output as they designed it, and add your own line outputs. Since they haven't fitted the line output driver circuitry that the more expensive model piano has, your simplest approach is to get some audio-coupling transformers and wire them across the speaker terminals, perhaps with a resistive attenuator pad between them, and add two extra ¼″ phone connectors near the headphone socket.
Don't be tempted to try and wire line output jacks directly to the speaker wiring, both the positive and negative speaker terminals are directly driven by the amplifier in differential mode. They don't just drive the positive and ground the negative. Joining any of the left and right speaker wiring together is very likely to damage the internal amplifier.
Using audio transformers allows you to create a floating balanced output, that can also have an unbalanced lead plugged into it without any problems.
(3) Yet another alternative is a slight variation to the second idea, but instead of tapping across the speaker outputs, you can tap across the headphone socket audio signals. Although this will be a lower signal voltage, but that might actually suit the equipment you're plugging into.
In my piano's review page I mentioned a stereo splitter circuit I'd made for separating the left and right audio from a headphone jack into two separate connectors, and providing the option for a mono-mix of both channels when only one jack is plugged into the output. While this is feasible to do with a low current headphone output with some resistive coupling, directly summing together left and right speaker amplifier drivers together would be a bad thing to do.
If you were simultaneously listening to it's headphone output, you may hear this monofication happen in the headphones any time the left and right audio signals were joined together through the audio transformers, though this would depend on the impedances of the transformers and headphones. I didn't notice it with mine. And with the switching scheme my circuit uses, this is any time that something isn't plugged into both line sockets. An alternative switch wiring would be to only bridge left and right together when just a single jack is inserted. This is easily done with common ¼″ jacks with built in DPDT switches, but a bit more of a tangle of wiring than the simpler method I used treating them as DPST switches which open when a jack is inserted.
Other notes
Plugging a mono unbalanced jack lead into a stereo TRS socket will short out the ring (right audio signal) to the sleeve (ground). Many headphone outputs can handle this fine, since there usually is a resistor is in-line with the signal feeds, though not always. This piano should be fine if that happens, it does have series resistors in the signal path (according to the service manual). You won't get a mono signal though, you'll just get the left audio by itself, and the right audio is shorted out.
Plugging a balanced TRS jack lead into a stereo TRS socket will result in a left minus right signal with wierd audio response.
It isn't necessary to add left and right together for a mono output, you can simply use one channel by itself. The left side is skewed slightly towards the bass string end of the piano, and the right side is skewed slightly to the treble end (the same for the other non-piano voices). It's not a striking difference, though, but I thought it sounded slightly better with both signals summed together. Particularly with the stereo chorus effect that some of the voices have.
Warnings
To get inside the piano you have to remove all the screws from the bottom (there's about 50 of them). And you'll have to be careful re-inserting them when reassembling it, as they're self-tappers going into plastic. If you force them in, instead of lining them up with the thread they originally bit into the plastic, you're going to chew out the plastic. Also don't wrench them in with high torque.
The bottom of the casing is attached to the top by a wiring harness. There's two boards in the bottom shell (the main board that does everything, and a board with the connectors), they're joined to the keyboard in the top half, with two very short ribbon cables at the rear side of the chassis. So place the keyboard upside down on a padded surface, unscrew it, carefully hinge open the base, opening up the keyboard side and keeping the back halves together.
Then, you can either just prop up the two halves still joined together, or carefully unplug the connectors.
The cables have been wrapped in a soft foam material, so that they can't buzz against anything with sympathetic vibrations as you play. You should do something similar with any added wiring. Or ensure that it stands free and can't touch anything.