I get them, too. Thousands of them. As stated above, they are no trouble in the lawn. Once decapitated, they don't come back. Try to pull them out of the garden beds before they get more than four or so leaves - they very quickly develop a root system and yanking them later, although easier, will disturb the soil around your plants. They will sprout in damp mulch but do come out very easily. I've even had them grow in just a tiny bit of guttercrud in the eavestroughs. These things seem endless but are usually conquered by end of June :)

I so wish the local animal control, or fish and game would come take care of the skunk I accidentally caught in my life trap (intended for cats that kill the yard birds). Anyway, I called local, state, fed. and they all said the same, "good luck." So this poor skunk is slowly starving/choking to death, because I'm cowardly and don't want to get sprayed or have the front yard stink for a month...so I have to find a way to deal with this! If the law, which I doubt, says I can't "relocate", then I'm left with killing the poor thing! This is going to haunt me in my nightmares! As for Kimmsr and her "well written" and well-researched input: state laws vary widely, it's best to call and find out if they'll help you before doing anything! If your state, like mine, won't help, here is a Youtube video that I think is the most humane I've seen: https://www.youtube.com/watch?v=E9F16vTJXbk  

I used a combination tactic - and let me just tell you, I had no clue how many rocks, tree trunks and random other stuff was hidden under the mountain of English ivy - dig up and move or discard the dirt from the excavation around the roots, at least a foot down and throughout the removal area; pull the small pieces and make cuts with a hand saw in the bigger ones; immediately upon cutting apply (carefully) either salt mixed with a bit of water to make it almost like a paste or roundup for woody plants/stumps; wait for the thicker roots to begin dying; pull out as the plant begins to make it easier by being dead. Whether you use salt or roundup you will need to replace the dirt around the area, which is why I suggest moving as much as you can to a ‘safe part of the yard’ elsewhere and discard that which you have remaining in the areas affected by the process with the treatment. I did the flower bed areas around my patio when living in a SoCal townhouse and it took 6+ months to do it all on my own - the funny part is that the original ivy was planted at least 50 yards away. That stuff spreads in an unbelievably fast way, I will never not protest anyone planting it where my yard will be affected ever again. And I was lucky that it hadn’t started climbing the walls because it’d been planted as groundcover so the landscaping crew regularly took a trimmer to it to keep the height down - initially I’d hoped that the crew would do the removal but for those ‘exclusive use common area’ flower beds, it fell to me to do it.

First, read the bag of the product and see what it is intended to kill. Surely, it will not kill any existing weed grasses (as you're showing us is your weed problem.) Let it do its job. It very well may take care of some broadleaved weeds. Usually results are not instant so give it time as per what the directions call for. How many times do you want to reseed the lawn? If you'd prefer to do it once, hold off and prepare for a late summer/fall seeding. Usually, one gets better results ... a more durable product. Meanwhile, just mow what you got. Instructions for creating a lawn are highly dependent on one's location. Usually, unless one has an automatic irrigation system, newly seeded lawns are prone to failure as soon as hot weather sets in. A fall seeded lawn has many months of root development prior to hot weather.