Random writes and/or multiple zero-fills are just a waste of time. They don’t achieve anything, they’re just a placebo. Plenty of people/procedures recommend to do it, but they’re absolutely pointless in the real world. Once your disk is full of zeros, it doesn’t matter what came before.

Don’t trust me? If the US government was unable to recover the content of a drive related to Julian Assange’s case after a single zero-fill, I think you’re safe:

Johnson testified that he found two attempts to delete data on Manning’s laptop. Sometime in January 2010, the computer’s OS was re-installed, deleting information prior to that time. Then, on or around Jan. 31, someone attempted to erase the drive by doing what’s called a “zerofill” — a process of overwriting data with zeroes. Whoever initiated the process chose an option for overwriting the data 35 times — a high-security option that results in thorough deletion — but that operation was canceled. Later, the operation was initiated again, but the person chose the option to overwrite the information only once — a much less secure and less thorough option.

All the data that Johnson was able to retrieve from un-allocated space came after that overwrite, he said.

In the case of an SSD, random writes or zero-fills don’t work at all, though: they are not guaranteed to actually fill the disk with zeros (and most likely won’t), while at the same time wear the drive. For SSDs, you should run a secure erase command that’ll instruct the SSD to reset all its cells to their default state.