How do I solve a non-linear linked system of equations

so I need to solve for chemical equilibrium of several product species in the combustion of CH4 and O2, so I am solving for the following unknowns [n_CO2,n_H2O,n_CO,n_OH,n_O2,n_H2,n_O,n_H] using the following equations

hydrogen balance 0=.5n_H2O+n_OH+.5n_H2+n_H-4

carbon balance 0=n_CO2+n_CO-1

Oxygen balance 0=.5n_CO2+n_H2O+n_CO+n_OH+.5n_O2+n_O

all of the previous equations were obviously linear, but now we get to the linked non-linear equations, in the following equations P is a known pressure, k_pn are constants that are also already known, and n is the sum of all the unknowns

CO+O<->CO2

0=n_CO2/(n_CO*n_O)-(P/n)*k_p1

OH+H<->H2O

0=n_H2O/(n_OH*n_H)-(P/n)*k_p2

2O<->O2

0=n_O2/(n_O^2)-(P/n)*k_p3

2H<->H2

0=n_H2/(n_H^2)-(P/n)*k_p4

O+H<->OH

0=n_OH/(n_O*n_H)-(P/n)*k_p5

I know the upper and lower limits of each unknown, so additionally, how would I specify those in whatever solver I would end up using?