About 'coeffs' and 'solve'

Assume that I have r:= -6x+3y+23x²-4xyz+7z² . By using coeffs(r,x,'k') I can find the coefficients of 1, x, and x². 

What should I write to get the conditions that make the coefficient of x zero? How can I just pick the coefficient of x, and solve it. 

I have several coefficients but the answer of this question will help me.