How can you solve this type of (not quite linear) diophantine equation in 2 variables?

Question

Is there a general technique to find solutions of this type of equation?

555555=t+2rt+r

I'll provide the only answer I know in the comments.

Thanks.

Answer 1

$$ 2rt + r + t = N $$ $$ 4rt + 2r + 2t = 2N $$ $$ 4rt + 2r + 2t + 1 = 2N + 1 $$ $$ (2r+1)(2t+1) = 2N + 1 $$