Solving for the equilibrium points of system of equations 
HIV inflicts its damage by
  infecting healthy CD4 + T cells (a type of white
  blood cell) that are necessary to fight infection. As
  the virus embeds in a T cell and the immune system
  produces more of these cells to fight the infection,
  the virus propagates in an opportunistic fashion. Normally T cells are produced at a rate $s$ and
  die at a rate $d$. The HIV virus is present in the
  bloodstream in the infected individual. These
  viruses in the bloodstream, called free viruses, infect
  healthy T cells at a rate $\beta$. Also, the viruses reproduce
  through the T cell multiplication process or
  otherwise at a rate $k$. Free viruses die at a rate c.
  Infected T cells die at a rate $\mu$.

A simple mathematical model to describe how the HIV/AIDS virus infects healthy cells is given by the following equations:
$$\begin{align}\frac{dT}{dt} &= s-dT-\beta T v \\ \frac{dT^*}{dt} &= \beta T v - \mu T^* \\ \frac{dv}{dt} &= kT^* -cv\end{align}$$
I am told that the system has two equilibrium points given by
$$(T_0, T_0^*,v_0) = (\frac{s}{d},0,0)$$ and 
$$(T_0, T_0^*,v_0) = (\frac{c\mu}{\beta k}, \frac{s}{\mu}-\frac{cd}{\beta k}, \frac{sk}{c\mu}-\frac{d}{\beta})$$
I am asked to prove that the equilibrium points are the ones shown above but I am having trouble proving this after setting the derivatives equal to $0$. I can obtain the first equilibirum point easily if $\mu$ is zero but otherwise not. How would I solve this system for the two equilbirium points? My differential equations knowledge is quite rusty. 

Setting the equations to zero gives:
$(1)\space   0 = s-dT-\beta T v $
$(2)\space0 = \beta T v - \mu T^*$
$(3)\space 0 = kT^* -cv$
My plan to solve the simultaneous equations here is to 


*

*use (3) to get $T^*$ in terms of $k, c, v$

*plug this $T^*$ found into (2) to get $T$ in terms of $v, \beta, \mu, c, k$ when $v\ne0$ 

*use (1) to get $v$ in terms of $s, d, \beta, \mu, c, k$

*finally use the $v$ found back into our found $T$ and $T^*$ equations


This gives the second equilibrium point once simplified as $(T, T^*, v)$
