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

No such thing as cancelling actually exists. What you do in those moments is to divide both sides of an equation by the same value. This means, cancelling like this:
$2t^2 + t^3 = t^4$ to $2t + t^2 = t^3$
Is actually a shortcut for:
$2t^2 + t^3 = t^4$ to $(2t^2 + t^3)/t = t^4/t$ to $2t + t^2 = t^3$
And you can only do that by assuming $t \neq 0$, so you discard that solution by doing such operation. Perhaps $0$ would still be a valid solution if the exponents are $> 2$ in each term (so $0$ would still be a valid root for them) but you should never assume that.
