How to factorize $2x^2+5x+3$? I'm doing pre-calculus course at coursera.org and I'm in trouble with this solution $$2x^2 +5x +3 = (2x+3)(x+1)$$
By trial, using ac-method I got stuck:
$$
ac = (2)(3) = 6\\
6 + ? = 5 \Rightarrow~ ? = 5 - 6 = -1
$$
Then,
$$2x^2+6x-x+3 = 2x(x+3)-x+3$$
At this point I could not get the answer, any help?

Complete squares:
$$2x^2+5x+3 = 2(x^2+2\alpha x + \alpha ^2) + (3- 2 \alpha ^2)$$
where $\alpha = \frac{5}{4}$. Then
$$(x+\frac{5}{4})^ 2 = \frac{1}{2}\left(\frac{25}{8}-3\right) $$
$$x+\frac{5}{4} = \pm \sqrt{\frac{1}{16}} $$
$$x= \frac{-5}{4} \pm \frac{1}{4} = \frac{-5 \pm 1}{4}$$
$$ x\in \left\{-1, \frac{-3}{2}\right\}$$
Therefore,
$$2x^2+5x+3 = (x+1)(2x+3).$$
