EDIT: I read somewhere that it needs 50MB of free space on the partition. Maybe you can first assign a drive letter using disk management and see if you can free up some space.
I had this “Something went wrong” & “unable to install on partition” error when I tried to upgrade a Laptop with Windows 7 Home Premium 64-bit installed. This laptop is from late 2011, and had Windows 7 pre-installed by the manufacturer.
This cryptic error, in my case, just meant that the hidden reserved system partition that Windows 7 creates on install was too small/full for Windows 10.
In earlier versions of Windows 7 this partition would be created with a size of 100MB. In Windows 8 I mostly see this partition with a size of 400MB.
So what to do? Expand this hidden system partition from 100MB to at least 400MB. To be safe for the future I expanded it to 800MB.
Now this is not something you can do from within Windows, because the C partition will have to shrink AND move to the right to make room to expand the system partition.
I suggest using a partition manager to do this. I had success using the free Minitool partition manager.
http://www.partitionwizard.com/free-partition-manager.html
First select the C partition and shrink by 700MB and move it to the right so that the free space comes available in between the small SYSTEM partition and the C partition. Then next select the SYSTEM partition and expand by 700MB until the free space is gone.
Now click the execute button, the software will tell you it must reboot to execute these actions.
Go ahead reboot, and then wait for some time (could take up to hours on big and slower drives) for the software to finish. You get a nice progress bar. For me it took 10minutes on an SSD.
When it’s finished it will boot Windows and you can check in Disk Manager if everything looks good. You can then uninstall or keep the software and start your Windows 10 Upgrade again.