Question: 6 equations 5 unknowns

Regards,

I am trying to solve a problem in theoretical applied mechanics in which I need to find the solution for 5 unknown but I have 6 equations. None of the equations is redundant and I need the solution of the variable to satisfy each of the equations.

These are the equations 

24-52*L^4*m[0]*Omega^2*(R+1/2)/EI[0]-168*beta[1]-52*F*L^2/EI[0]+104*beta[2]+(120+72*beta[1]+104*L^4*m[0]*Omega^2*R/EI[0]-504*beta[2]+312*beta[3]+84*L^4*m[0]*Omega^2*(R+1/2)/EI[0]+84*F*L^2/EI[0])*x+(240*beta[1]+144*beta[2]-1008*beta[3]+624*beta[4]-12*L^4*m[0]*Omega^2*(R+1/2)/EI[0]-126*L^4*m[0]*Omega^2*R/EI[0]+78*L^4*m[0]*Omega^2/EI[0]-12*F*L^2/EI[0]-26*L^4*m[0]*omega^2/EI[0])*x^2+(16*L^4*m[0]*Omega^2*R/EI[0]-84*L^4*m[0]*Omega^2/EI[0]+14*L^4*m[0]*omega^2/EI[0]+400*beta[2]+240*beta[3]-1680*beta[4]-20*F*L^2/EI[0]-20*L^4*m[0]*Omega^2*(R+1/2)/EI[0])*x^3+(600*beta[3]+360*beta[4]+25*L^4*m[0]*Omega^2*R/EI[0]+10*L^4*m[0]*Omega^2/EI[0]-L^4*m[0]*omega^2/EI[0])*x^4+(840*beta[4]+15*L^4*m[0]*Omega^2/EI[0]-L^4*m[0]*omega^2/EI[0])*x^5

This equation is in series with respect to x. Each coefficient in front of x^n has to be zero.ta[2]*beta[3]*beta[4]*omega^2

is there any mathematical procedure I could use to solve simustaneosly for all of these? I have tried many things but I have had no succes until now. Any help will be very appreciated it. Thanks in advance