Please help

How do I solve the quadratic equation 3x^2 + 5x + 2 =0

Please explain the steps-I really don't get this

By factoring:

3x^2 + 5x + 2 =0
3x²+3x +2x+2 = 0
3x(x+1) + 2(x+1) = 0
(3x+2)(x+1)=0
So
3x+2=0 or x+1=0
Solve for x in both cases.