Factors after using quadratic equation and normal factorization process in algebra

i want to know will the factor be same for an equation despite using any method to make them. i use quadratic formula to make factors for 2 equations and normal factorization but the answers are different.

You should not get different answers. The factorization is unique in \mathbb{R} up to multiplying each term by a unit and compensating.

Here’s an example of what I mean in the second sentence.

(3x^2 + 1)(2x^2 + 7) = (3x^2 + \frac{21}{2})(2x^2 + \frac 23)

You can, however, see that this is just shuffling a constant factor around so nothing changes.

(3x^2 + 1)(2x^2 + 7) = (3x^2 + \frac 1u) (2x^2 + 7u) is equivalent for all u \neq 0

Maybe it’d be helpful for you to show your work. My above response is just my interpretation of what your actual question is.