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3\left(-16g^{2}+1\right)
Factor out 3.
\left(1-4g\right)\left(1+4g\right)
Consider -16g^{2}+1. Rewrite -16g^{2}+1 as 1^{2}-\left(4g\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(-4g+1\right)\left(4g+1\right)
Reorder the terms.
3\left(-4g+1\right)\left(4g+1\right)
Rewrite the complete factored expression.