Question: Solving a Quadratic Diophantine Equation with 3 variables

How do I find integer solutions to this non-linear equation:


8= 7(x^2+y^2+z^2)+2x+4y-8z.


Tried isolve and it wasn't working. (I guess too many variables?)


Also, if f(x,y,z) is the RHS, how do I write a loop that finds integer solutions to f(x,y,z)=c for |x|,|y|,|z|< N, say?

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