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Then, consider what would have to be added to the right side to keep both sides equal.

4?

Right, adding 4 inside the parentheses on the left yields
\(\large 3(g^2-4g+4)=-4 + ?\)

so 4 completes the square then?

47

47?

What happens when you distribute that 3 back into those parentheses on the left?

3g^2-12g+12

oh got it thanks!