In some SUVAT questions, they ask for 2 time solutions and I can only find 1. What am I missing?

Let's say we are trying to work out how long it will take for a ball to be caught after it has been thrown straight upwards. If we set the final displacement to be zero (S=0) and solve S=UT+0.5AT², it appears that we only get one value for T. However, there will always be a step in your workings when you can cancel a T from both sides of the equation, for example: 5T² = 100T can be simplified to 5T = 100. In this step, we miss out a solution that T=0! This corresponds to when the ball is just about to be thrown so is still in our hands (hence we have a solution for zero displacement!)