In such case, I would recommend running boot-repair.
https://help.ubuntu.com/community/Boot-Repair
If Ubuntu is indeed installed correctly onto its own partition, boot-repair will find it, along with the other OS (Win10). It will install grub into the boot partition.
Boot-repair can be downloaded and run from a live usb. So using the usb medium you used to install Ubuntu, repeat the procedure to boot your computer from the usb stick, hit "try ubuntu" instead of "install ubuntu" and follow the instructions in the link.
EDIT:
Using the pastebin information you provided, I could tell that
1. Ubuntu seems to be installed on disk, on the same disk as your Windows OS on its own partition.
2. The boot-repair session was run , I presume, from a live session usb booted in legacy mode
Therefore, I suspect your problems arise from having installed Ubuntu from a legacy mode booted usb. This won't work well with Windows 10, which in standard configuration always is EFI booted.
The work around you described tries to alter this, by forcing Win10 to boot in CSM/Legacy. But I advice the other way around: re-installing Ubuntu in EFI.
Steps:
1. Boot into BIOS. Make sure every usb device is EFI booted
2. Boot from ubuntu live usb, confirm EFI boot.
3. Re-install ubuntu in sda6 partition
(4. If needed, re-run boot repair from a EFI booted live usb)