(12n + 6)n = 180 (n - 2). Find n

n=12   n=5/2

Step-by-step explanation:

(12n + 6)n = 180 (n - 2)

Distribute

12n^2 +6n = 180n -360

Subtract 180 n from each side

12n^2 +6n - 180n = 180n-180n -360

12n^2 -174n =  -360

Add 360 to each side

12n^2 -174n+360 =360  -360

12n^2 -174n+360 =0

Divide by 6

12/6n^2 -174/6n+360/6 =0

2n^2 -29n +60 =0/6

2n^2 -29n +60 =0

Factor

(n - 12) (2 n - 5) = 0

Using the zero product property

n-12 =0   2n-5=0

n=12   2n=5

           n=5/2