The given expression appears to represent a quadratic expression: ...

The given expression appears to represent a quadratic expression:
20n² − 60n − 35

The purpose of the code (or task) is likely to factor the quadratic expression completely.

Steps the code or process might take:

1. Simplify common factors: Factor out the greatest common factor (GCF) of all terms in the expression. Here, the GCF is 5, so: [ 20n^2 - 60n - 35 = 5(4n^2 - 12n - 7) ]

2. Factor the quadratic expression: The remaining quadratic expression 4n² − 12n − 7 can potentially be factored further:

   • Multiply the coefficient of (n^2) (4) by the constant term (-7), which equals -28.
   • Find two numbers that multiply to -28 and add to the middle coefficient (-12). These numbers are -14 and 2.
   • Rewrite the middle term using these two numbers: [ 4n^2 - 12n - 7 = 4n^2 - 14n + 2n - 7 ]
   • Group terms and factor by grouping: [ 4n^2 - 14n + 2n - 7 = (4n^2 - 14n) + (2n - 7) = 2n(2n - 7) + 1(2n - 7) ]
   • Final factorization: [ 4n^2 - 12n - 7 = (2n - 7)(2n + 1) ]

3. Combine with the GCF: Multiply the factors by the GCF (5): [ 20n^2 - 60n - 35 = 5(2n - 7)(2n + 1) ]

Final Answer:

The code (or task) factors the quadratic expression completely into: [ 20n^2 - 60n - 35 = 5(2n - 7)(2n + 1) ]