how do i simplify 2p^2+3p+1=0

how do i simplify 2p^2+3p+1=0

$$\small{\text{$
\mathbf{2p^2+3p+1=2\left(p+\dfrac{1}{2}\right) \left( p+1\right)=0
}
$}}$$

2p^2+3p+1=0

You need 2 numbers that mult to 2*1=2  and add to 3     That will be  2 and 1

now replace 3p with 2p+1p

$$\\2p^2+3p+1=0\\\\
2p^2+2p+1p+1=0\\\\
$now factor in pairs$\\\\
2p(p+1)+1(p+1)=0\\\\
(2p+1)(p+1)=0\\\\
2p+1=0\;\;or\;\;p+1=0\\\\$$

And you can finish it :)