This is a quadratic equation.
Calling the short side 'x', you've got x(x+3)=88.
Multiplying out of brackets gives x²+3x=88.
Put it all on one side, because with quadratics that's just what you do: x²+3x-88=0
Factorise it: (x+11)(x-8)=0
There's no short way to factorise things, you just get a knack eventually.
Anyway, as (x+11)(x-8)=0, that means that either x-11 or x-8=0, because anything times 0=0.
So, if x+11=0, rearranging gives x=-11. This would be a valid solution if it was a pure question, but as the question is applied to measurements, negative values are ignored.
This leaves x-8=0, which when rearranged gives x=8, which is the answer.
Your room is 8m wide and 11m long.

Sorry if I've been too complicated or patronising.

oh my days - mathsy - you're clever- how old are you?

You may also remember, given the roots of a quadratic equation, the equation can be got thus:-

x² -(Sum of the roots)x + (products of the root) = 0