Need help solving these simultaneous equations, anyone with a pen and paper?

Firepanda
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Solve

-r*(T^2 + T + 6) + 1 = 0

4r*(T^2 + T) - T = 0

For T and r

One solution is T=0 and r=1/6

There are 2 more.


I have T = +- i/(2)0.5 and r = 1/[4(1+T)]

But MATLAB is disagreeing with my solutions, can anyone rectify them for me please?
 
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ah nevermind, foudn my mistake early on, sorry for anyone bothering to attempt it I've done it (after 3 hours :/ )
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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