Is this a good build for gaming?

Rapajez

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Assuming we're talking a 1080p monitor, or less, that should get the job done. Some of the settings may need to be cranked down in more demanding games.

I'd switch to a newer, higher reviewed mobo, like this: Gigabyte GA-970A-UD3P

If you can spare a little money, the R9 280 isn't much more, and performs a little better in new games.

Finally, the PSU isn't one of the best. Check out the XFX series, 550W should get you by, 650W may be safer for overhead.
 

Rapajez

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AKA:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($98.99 @ Amazon)
Motherboard: Gigabyte GA-970A-D3P ATX AM3+/AM3 Motherboard ($69.99 @ Newegg)
Memory: G.Skill Sniper Series 8GB (2 x 4GB) DDR3-2133 Memory ($74.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($53.98 @ OutletPC)
Video Card: Sapphire Radeon R9 280 3GB DUAL-X Video Card ($189.30 @ Newegg)
Case: Corsair 200R ATX Mid Tower Case ($39.99 @ Micro Center)
Power Supply: XFX TS 550W 80+ Gold Certified ATX Power Supply ($59.99 @ NCIX US)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($102.98 @ Newegg)
Total: $670.21
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-08 16:15 EDT-0400
 
Solution

Rapajez

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You shouldn't need a BIOS update for that CPU, but it's always good to have the latest BIOS.

You can go to the Gigabyte's website to download the latest BIOS update. From there, you should be able to get a version that runs right from Windows, or a version you copy to a USB drive or CD, and run on a restart.

When you first start the PC, you press "F2", or whatever is on the screen, to enter the "BIOS". From there, you look for the "update BIOS" screen.