Can you put my goldfish back into the tank right after changing water?

No, you should not put your goldfish back into the tank right after changing water. The new water may have different parameters (e.g., temperature, pH, hardness) than the old water, and this can shock your goldfish and cause stress or even death. It's best to let the new water sit for at least 24 hours before adding your goldfish back to the tank, or use a water conditioner that will neutralize any harmful chemicals.