How to Estimate the Input for a Convolution Given the Filter (Impulse Response) and the Output of the Convolution I understand how to find the output from the input with an impulse response, but how can I go about finding the input if given the other two?

I have $y[n] = [-1, -1, 11, -3, 30, 28, 48]$ and $h[n] = [-1, 2, 3, 4]$ 

How can I go about finding $x[n]$? 

I know very little about signal processing, so if you don't mind giving an easy explanation, then I appreciate it. Or, if it's possible to do an example, that's better.

EDIT: I think that if I know $y[n]$ I can guess what $x[n]$ would be by multiplying and summing the results, but I'm not sure how to figure out the length of $x[n]$.
Mathematically, here is the demostration for what you want to do:
y[n] = x[n]*h[n] (This is a convolution),
Applying convolution theorem you can prove that:
Y[f] = X[f]*H[f] (this is an ordinary product),
Then:
X[f] = Y[f]/H[f],
Now if we apply fourier inverse transform to X[f] you can have x[n].
Implementing this in matlab can be pretty straightforward now.
Cheers