$Q = mc\,\Delta T$ is one fact wearing four outfits. Solve it for $m$ and it weighs the water a heater warmed; solve it for $\Delta T$ and it predicts the climb; solve it for $c$ and it does something lovely — it identifies materials). Measure the heat in, the mass and the climb, compute $c = \dfrac{Q}{m\,\Delta T}$, and the data sheet tells you whether your mystery block is aluminium (900), iron (450) or lead (130). Detectives with thermometers.

Your safety rail when rearranging is the units. Whatever you solve for, push the units through: if they refuse to cancel down to the answer's units, the rearrangement is wrong — no appeal. (Units that do work out never prove you right — the check only works one way — but it catches nearly every upside-down fraction before it costs you.)