1. **State the problem:** Factorise completely the expression $6x^2 + 25 - 9$. 2. **Simplify the expression:** Combine like terms $25 - 9$. $$6x^2 + 25 - 9 = 6x^2 + 16$$ 3. **Rewrite the expression:** Now we have $6x^2 + 16$. 4. **Factor out the greatest common factor (GCF):** The GCF of $6x^2$ and $16$ is $2$. $$6x^2 + 16 = 2(\cancel{3x^2} + \cancel{8})$$ 5. **Check if the expression inside the parentheses can be factored further:** $3x^2 + 8$ cannot be factored further over the integers. 6. **Final answer:** $$\boxed{2(3x^2 + 8)}$$