SSD devices have a special command ATA Secure Erase that will instruct the firmware to release all data stored on every sector of the disk. According to NIST (U.S. National Institute for Standards and Technology), ATA Secure Erase is an effective and secure way to meet legal data sanitization requirements against attacks up to laboratory level.
It works different on SSD devices with and without encryption.
On devices that does not perform encryption, the controller is instructed to send a voltage spike to all sectors, resetting every block of data.
On devices that employ transparent encryption, only the key is changed. There's no way to recover the key, and even if the data is not changed, it's impossible to decrypt without the proper key.
Is possible to use hdparm on Linux to execute a Secure Erase on a SSD.
A study from Michael Wei et al describes a lot of ways to properly erase a disk, and shows that some firmware bugs and missteps can prevent the disk from being secure erased. So, a hybrid approach (Data overwriting and ATA Secure Erase) would suffice to destroy the data.