How do you solve an engine vibration problem?

At start up vibration is noticed and felt over whole vehicle. Rattles the front grille. Smoothes out somewhat at higher rpms but I can feel the vibration through accelarator even at higher rpms. Have jacked up front of engine about an inch and vibration reduces significantly.

THANKS FOR YOUR ANSWER. DO YOU THINK REPLACING THE AFTER MARKET MOUNTS WITH THE GM MOUNTS WOULD MAKE A SIGNIFICANT DIFFERENCE? I EVEN THOUGHT ABOUT TRYING TO PUT SOME TYPE OF HARD RUBBER SHIMS ON THE FRONT MOUNTS SINCE RAISING ENGINE SEEMS TO HELP. WHAT DO YOU THINK ABOUT THAT IDEA? KNOW THAT IS "SHADE TREE" BUT I AM OUT OF REPAIR MONEY AND NEED TO GET THIS FIXED!

Trailblazer with 180000 miles started a BAD engine vibration. 02/2015
While in Drive the engine vibration was loud and in Neutral it ease down a bit.
Parts from Rock Auto. Replaced the fuel pump, fuel filter, water pump, thermostat, almost every sensor in the engine and outer transmission were replaced. Next, the Trans Mount and Engine Mounts were replaced with WESTAR brand. THE Vibration went almost away but it was still there, Not as bad but it was there.
Now a month ago this year 2017 with the Engine now 230000 the Vibration came back. Changing the plugs, coils and boots didn't help. FINALLY I ordered the AC DELCO motor mounts from Rock Auto installed the mounts and is working like NEW! NO more Engine Vibration.
Do NOT install aftermarket motor mounts, they work fine for -+ 1 year and before you know is back to square one.

Hello Guys! Just giving my 5C I struggle fuguring what was wrong with my truck it vibrated on D only! I checke with my OBDII for any signs of vaccum leaks, Fuel shortage or leakage but everything looked fine! Vibration was even all a cross meaning that it didnt feel like an specific cylinder was doing it (heads were new it overheated on me over fan clutch) anyways air intake Tem looked fine, MAP sensor fine as well and no Engine light, O2 responded fine as well so I knew all elements that control air/fuel mixure were fine so it pointed to something else, may be tranny mount or motor mount so I got under neath and checked tranny first I used my floor jack pipe to push up the tranny but nothing change, I noticed it had a bracket that hold the exhaust and it attaches to the tranny mount as well so I got the pipe under that bracket and pushed it up and to my surprise vibration went a way so I did it a few times to make sure that was working and it did, by pushing that bracket up I was pushing the Engine as well so it was clear what the problem was! Motor Mounts! I Order new from Dealer Gmpartsdirect $159 pair I didn't know if originals are AcDelco or Delphi so I didn't want to take the chance! Anyways I replaced them in about an hour and truck doesnt vibrate anymore! I can't even tell that is On! I bit of the work I did to replace them, no need to take any A arm apart or nothing! By each Tire there are 3 Big bolts that hold the Mount Bracket remove them from both sides, I used a 2X4 pc of wood underneath the oil pan/ put it on the side where the pan is harder, lift it so its easier to remove side bolts, after all 6 bolts are removed you need to lift the engine until you can lift the bracket ( it has a lip thst holds it in place) tgen just keep lifting until it pops out, replace with new mounts and put it back the reverse way, when you replace the first one dont tighten the top bolt you need to lift it for the other mount, install the other mount and your done! Make sure you don't forget the hear shield on the passanger side as I did or you will have to remove it again!? Good luck Guys
PD
If your vibration is Even meaning you dont feel and missfire then go this route above!

If you want to test the head/ gasket there is different ways
1- leak down Test
2- smoke through Radiator, if water gets through smoke will even easier! Radiador empty use a radiator tester cap which has plug, hose to add presure and pump smoke, Ebay or many other sites sell it!
3- check for spark plugs redish color/water
4- check oil cap for any white film
And oil dipstick it self.

Easiest way to know if it is your mounts lift muffler with a bar close to engine, if it gors a way forget all other things you know the reason!

Engine vibrates particularly at about 1800rpm, also quite noticeable exhaust resonating boom. Vibration felt through steering wheel, gear shift, etc. Noticeable shudder when starting engine and switching off. All attempts to remedy the situation so far failed - including: new exhaust from behind cat to tail-pipe; new pipe joint springs and gasket from manifold; new back engine mount and new top engine mount. Tested a theory that, having been laid-up for some years (hence very low mileage), some sludge may have attached itself to crankshaft; by giving engine extra flushing prior to oil change. Question: would it be worth the additional expense of replacing both front engine mounts, in the hope that this would cure the vibration, or would this be throwing good money after bad. Car is, otherwise, in remarkably good condition for age, albeit without p.A.S. / E.W. / C.L. / Etc.

Its worst when I put in drive and press the break. Recently I change the motor mounts and the balancer, but the vibration still felling in the hood.