salt hydrolysis and pH calculations
The general approach to solve acido-basic equilibrium problems is:

respecting charge balance and charge conservation
respecting mass conservation
respecting dissociation equilibrium constants for acids, bases and water itself.

Generally, it leads to a set of nonlinear equations for a set of independent variables. The application of a substitution method usually results to a polynomial equation for $\ce{[H+]}$ of the second up to the forth order. The latter is hard to solve analytically.
Fortunately, in many scenarios, there can be made justified simplifications, like

neglecting water autodissociation
neglecting concentration of one substance form wrt the other one or their sum.

That largely simplifies an equation to be solved.
E.g. to calculate $\mathrm{pH}$ of solution of acetic acid, ammonia, or sodium carbonate,
we can consider none of $\ce{H+}$, resp. $\ce{OH-}$ are created by the water autoionization and just negligible part of the compound underwent the acido-basic reaction.
E.g. for sodium acetate hydrolysis
$$K_\mathrm{b}=\frac{\ce{[HA][OH-]}}{\ce{[A-]}}\approx
\frac{{\ce{[OH-]}}^2}{\ce{[A-]}}\approx \frac{{\ce{[OH-]}}^2}{c_0}
 $$