algebra precalculus - Why does cancelling change this equation?

The equation

$$2t^2 + t^3 = t^4$$

is satisfied by $t = 0$

But if you cancel a $t^2$ on both sides, making it

$$2 + t = t^2$$
$t = 0$ is no longer a solution.

What gives? I thought nothing really changed, so the same solutions should apply.

Thanks