Why factoring with quadratic equation gives two different answers? I was working on a problem about induction, and I got stuck with a factorization:
$$(2n^2+7n+6)$$
If I find It's roots, I get $x=-2$ and $x=-3/2$. Then I can write it as: $$a(x+2)(x+\frac{3}{2})$$
But how could I find $a$? I don't have a solid background in this topic as I mostly ignored middle school mathematics and now I'm interested in it, been trying to search "how to factor using quadratic formula", the only thing I got right is that if I decide to factor the $2$, I get $(x+2)(2x+3)$ which now is the same parabola. What core topic I'm missing?

The coefficient $a$ is the coefficient of the degree-2 term, which tells you that $a=2$. Another way to see is evaluating at some point other than zero. For instance if you evaluate both expressions at 1, you get
$$
2+7+6=a\times 3\times \frac52=\frac{15a}2.
$$
This shows that $15=15a/2$ and so $a=2$.
