Here's a build that can help you win games in the Silver League with a rush strategy as Terran vs Zerg:

Start with a 14 Supply Depot, 15 Barracks, 16 Refinery.
As soon as you have enough resources, build another Refinery and an Orbital Command.
Make a Factory and start producing Hellions and Reapers.
As soon as you have a decent army, attack the Zerg base with your Hellions and Reapers.
Once you've damaged the Zerg's base, follow up with a Siege Tank and Marine push.
Add a Starport and a Raven to your army to help with air defense and map control.
If the game goes on, add more Siege Tanks and Marines to your army and keep pressuring the Zerg player.
This build focuses on fast aggression and map control, taking advantage of the Zerg player's lack of early game defenses. Good luck!
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