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?

The product of $2,\, 3$ is $6$, as you note.  The factors of $6$ which sum to $5$ are $\,2,\, 3.\;$  So we can write $$\begin{align} 2x^2 + 5x + 3 & = \color{blue}{2x^2 +} \underbrace{\color{blue}{2x} + \color{red}{3x}}_{= 5x} \color{red}{+ 3} \\ \\ &= \color{blue}{2x{\bf( x + 1)} } + \color{red}{3{\bf(x+1)}} \\ \\ & = {\bf(x+1)}(2x + 3)\end{align}$$
