Determine the real coefficients of a polynomial

I need to determine the real coefficients $a, b, c$ of the following polynomial:

$$P(x) = x^5 + ax^4 - 2x^3 - 6x^2 + bx + c$$

I know that $P(-2) = 9$, and the sum of the solutions (roots of the polynomial) is 3, and so is the product. I'm not sure if these last two conditions are correct, they sound like a typo?

Then I need to write the given polynomial by degrees of $(x - 1)$.

Now, I've tried going this way:

If $P(-2) = 9$, then

$$16a - 2b + c = 37$$

As far as I know, a quintic polynomial should have 5 real solutions? Therefore,

$$x_1 \times x_2 \times x_3 \times x_4 \times x_5 = 3$$ and
$$x_1 + x_2 + x_3 + x_4 + x_5 = 3$$

But where do I go from here? How do I formulate this into something that will probably result in a system of two equations with $a, b, c$? Then I can solve them with the first one.