 In this video, we provide the solution to question number four from the practice exam number two for math 1050. We're given the quadratic equation 3x squared plus 5x plus 2 is equal to zero, and we need to solve this quadratic equation. Now fortunately, it's in the standard quadratic form for quadratic equation, the right hand side is equal to zero. So we know the coefficients a, b, and c right here. We could use the quadratic formula if that we wanted to, we could try to complete the square. I'm going to see if there's some type of factoring that works here. Because if I bring the leading coefficient and the constant coefficient together, we get three times two, which is equal to six. I need factors of six that add up to be five, which admittedly the answer is already there. Just take three and two, like so. So then we can proceed to factor this thing, 3x squared, 3x squared plus 3x, we'll put in the first group. For the second one, we'll have a 2x plus a 2 in the second group there. So from the first group, we can pull out a 3x that leaves behind x plus one. From the second group, we can pull out a 2, which leaves behind x plus one. And so then finishing our factoring process, we get 3x plus two, and then we get x plus one is equal to zero. Using the zero product property, we said each and every one of these factors equal to zero. If you set the first factor, 3x plus two equal to zero, you would end up with a negative two-thirds to solve the linear equation. For the second one, if we set x plus one equal to zero, we end up with a negative one. So therefore, we found our two solutions, negative two-thirds and negative one. And so we see that the correct answer is E. Had we completed the square or used the quadratic formula, our calculation would have looked a little bit different. But when we were done, we would have still had these same two solutions, negative two-thirds and negative one.