If k=x+3/x-3, and k^2-k=12, find x. (show work)

Question

If k=x+3/x-3, and k^2-k=12, find x.  (show work)

mathmale · Answer

Hint:  the 2nd equation can be written in the form of a quadratic equation.  Do so, please, and solve that equation for the 2 different values of k.  Then subtitute those k values, one at a time, into the first equation.

anonymous · Answer

so then the quadratic equation is:  K^2-K-12=0  correct?

mathmale · Answer

Yes.  Now please solve that eq'n for k.

anonymous · Answer

can you give me another hint, this is helping me a lot.  
what is the value of K

mathmale · Answer

K^2-K-12=0 can be factored:  (k-4)(  ?  ).  Can you finish that?

anonymous · Answer

perfect, so then (K-4) and (K+3)  because multipled -4 * 3 = -12 and added = -1
this is very helpful.

anonymous · Answer

so then k1 = -3 and k2 = 4

anonymous · Answer

but then do i substitute back into the equation?