How can I factorise 2(x^2)+3x+1=0 ?

This quadratic equation is in the form ax^2+bx+c=0 (a=2, b=3, c=1), where there is a coefficient in front of X² term. First we have to multiply a and c. we then have to find two numbers z and y which multiply to give ac and add up to give b.I.e. zy=ac and z+y=b.
In the example case values 2 and 1 multiply to give 2 and add up to give 3. We then express the quadratic equation as 2(x^2)+2x+x+1=0 (Where the x coefficients equals z and y). Afterwards we see what we can factorise in our new quadratic equation. From the example we can factorise 2(x^2) +2x to get 2x(x+1) and we can't factorise anything else. Notice that after we factorise we have 2x(x+1) and 1(x+1). Here we have a factor (x+1) and we can then simply get another factor 2x+1. Our factorised quadratic equation is (2x+1)(x+1)=0.