$(5 - d) + (5 - d + 2d) = 14$ → $5 - d + 5 + d = 10 = 14$ → $10 = 14$, impossible.
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- Contradiction: $a + d = 5$ and $a + d = 7$ cannot both hold. Thus, no solution.
- But perhaps the problem meant the first term is $a$, third term is $a + 2d$, and their sum is 14, and second term is $a + d = 5$. Then:
- From $a + d = 5$, $a = 5 - d$. Substitute into $a + (a + 2d) = 14$:
- Hence, no such sequence exists.
- Final answer: $\boxed{\text{No such sequence exists}}$
- Question: Factor the expression $12x^3 - 18x^2 + 6x$ completely.
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