Well, the table goes like this for reaction aA+bB <-> cC+dD
Suppose that the reaction is going forwards so [A] and is decreasing. So let [F] be an arbitrary concentration of F.
Initial: [A] [C] [D]
Change: -aX -bX +cX +dX
Equilibrium: [A]-aX -bX [C]+cX [D]+dX
So X is a variable we have to solve. The coefficients in front of the X are the molar coefficients.
Then write down the mass action expression: [A]^a^b/[C]^c[D]^d = K
Then substitute the equilibrium values inside this expression and solve for K.
Sometimes if the stoichiometric coefficients are nasty and you might end up with quartics.
But that's rare.
Use assumptions when the K values are extremely large or very little.
Say its extremely small. So the concentration of A is likely to stay constant if it was large.
E.g. if A was 5 molar, and K = 10^-7. So final A is likely to be around 5.
Using assumptions is useful for weak acid/base calculations where K can be very small, such as for organic acids.