Amazing equations!!!

Algebra Level pending

Consider equations

(x-y)(x+2y)(2x+y)=160 AND x^2 + xy + y^2 = 28 AND (x-y)(x+2y)=k
Find the values of k (-21<k<21) such that all three equations meet simultaneously at a point. If the possible values of k are k1 and k2 then find |k1|+|k2| ...............that is sum of absolute value. PLEASE DONT GUESS OR USE INTERNET.. AND post your solution

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