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Solve for $x^2 + 7x +1 = 3n(x^2 + x +1), n \in \Bbb{Z}$

edit: I want to know what was[is] wrong with my question in the first place. Request to reopen and asking for reasons to put on hold in the first place not necessarily mean the same thing.

My this question was put on hold as off-topic because it lacks context. It also gives a link to how I can add context. The link gave the following points

  1. Include your work
    My response: I answered that question which I asked. I got a few hints from the comments which helped me. Should I give a summary of my solution it the question?
  2. Motivation for the question
    My response: I said in the details of the question that the original problem was a trigonometric equation which I solved but was stuck there.
  3. From where the question came from
    My response: It came from a book which is suppose to help me in my College entrance exam. But in this context, it is really irrelevant and rather obvious.
  4. Give your background
    My response: I did give my background. I am a high school student who is self-studying for the college entrance exam.
  5. Reference
    My response: None exist.

I am not criticizing the one(many) who put my question on hold because nobody has to answer my question as this site is run by volunteers. I am just curious. How can I improve my question?

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    $\begingroup$ Because you know exactly the context and motivation for your Question, you may not appreciate that your Readers are left in the dark about those matters or may even suspect that "in this context it is really irrelevant". Let me try to help you see what important information is lacking in the current form of the Question. You say (imperative) "Solve for..." but what follows is not the variable $x$ but the equation involving $x$ and $n$. According to your quantification $n$ is known to be an integer, but it's unclear if both $x,n$ are to be found, and what kind of value $x$ is. $\endgroup$ – hardmath Apr 15 at 4:37
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    $\begingroup$ In short, if you show how the algebraic problem is derived from a trigonometric one, that would likely clear up the confusion over what you really wanted. $\endgroup$ – hardmath Apr 15 at 4:39
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    $\begingroup$ I second hardmath's advice. Give a bit more detail about how you ended up with this equation. Or something else. The fact that you managed to solve the equation in the end yourself has a lot of weight, but in its present form the question itself is a bit sloppy. For those who don't want to click: the OP's answer currently has 4 upvotes. IMO the OP is NOT one of those high schoolers who want to outsource their homework. $\endgroup$ – Jyrki Lahtonen Apr 15 at 6:05
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    $\begingroup$ There are some tips in our guide for new askers. Not all the tips apply to your question. Anyway, the main thing is to show that you are serious about learning and doing math yourself. There are many ways of convincing the voters about that. To repeat, the question body should also show evidence of that. The simplest way may be to tell that originally you had trig equation A, and a substitution B (or whatnot) turned this into this algebraic equation. $\endgroup$ – Jyrki Lahtonen Apr 15 at 6:10

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