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 :)