We decompose quadratic coefficient 2 into two factors 1 and write it on the left, and constant coefficient 3 into two factors 3, 1 and write it on the right (as shown below).
^^^^^ 1,^^^3,
^^^^^2,^^^ 1,
Their diagonal line is cross. Multiply them and add them:
1* 1+2*3= 1+6=7; Exactly equal to the coefficient of the first term,
Then 2x2+7x+3; =( 1X+3)(2X+ 1)=(X+3)(2X+ 1)
This is also an effective and fast method to solve the quadratic equation of one variable. The key is your proficiency.