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Let $A \in \mathbb{C}$ be a nonzero complex number.

What is the solution of $x_1x_2x_3x_4x_5 + A = 0 $ in the field of complex numbers $\mathbb{C}$ ? Or more generally the solution of $x_1\cdots x_n + A = 0$ in $\mathbb{C}$ ?

Thanks for your attention guys :)

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    @Ted Please consider converting your comment into an answer, so that this question gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868).2013-06-10

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This CW post intends to remove the question from the unanswered queue.


As remarked in the comments the general solution of $X_1\cdots X_n+A=0$ is $\{(X_1,\dots, X_n)|X_1\neq 0,\dots, X_{n-1}\neq 0, X_n=-\frac{A}{X_1\cdots X_{n-1}}\}$ This follows by observing that if one of the $X_i$ is zero, then because of $A$ being non-zero, this will never be a solution and in the case of all of them being non-zero solving for $X_n$.