### Solving a simple system of equations

Hey Guys,

New to Sage and just trying to solve a simple system of equations. The system is below:

x,y,z,w,ha,hb,e,c = var('x y z w ha hb e c')

f1 = (c*(x+y)*(ha-x))-(e*x)

f2 = (c*(z+w)*(ha-x-z))-(c*z*(x+y)) - (e*z)

f3 = (c*(x+y)*(hb-y-w))-(c*y*(z+w)) - (e*y)

f4 = (c*(z+w)*(hb-w))-(e*w)

I want to find the equilibrium solutions, solving for x, y, z, w, when equations f1-f4 are equal to zero. So I try:

solve([f1==0,f2==0,f3==0,f4==0],x,y,z,w)

Unfortunately this causes Sage to hang (or it takes a remarkably long time to solve that I interrupt the process). This problem shouldn't be difficult to solve, but I am at a loss as to what to do. Perhaps I am going about this the wrong way??