we are solving for the expression (n + 4)^2 - (n - 2)^2 - 12n

>(n+4)^2 also means (n + 4)(n + 4), the same goes to (n - 2)^2, we have:

(n + 4)(n + 4) - (n - 2)(n - 2) - 12n

>Now let's factor (FOIL), we have:

(n^2 + 4n + 4n + 8) - (n^2 - 2n - 2n + 4) - 12n

(n^2 + 8n + 8) - (n^2 - 4n + 4) - 12n

>You thenuse polinomial operation, we have:

n^2 + 8n + 8 - n^2 + 4n - 4 - 12n

12n + 4 - 12n

> Our final answer is 4 since 12n - 12n = 0, and we are left with 4

Hope I helped......

First of all, you've provided an expression and not an equation. To transform the given expression into an equation, you must make it equal to zero or another algebraic expression.

We'll solve the equation `(n+4)^2 - (n-2)^2 - 12n = 0`

We notice that the difference between the first terms is a difference of two squares that could be written as the product:

(n + 4 - n + 2)(n + 4 + n - 2) - 12n = 0

We'll solve what's within the brackets:

6(2n + 2) - 12n = 0

12n + 12 - 12n = 0

12 = 0 impossible.

**Therefore, the given equation has no solutions.**