Solve the following equation:

(n + 1) + 3 (n - 1) = 2 (n - 1) (n + 1)

n = 0, n = 2

Step-by-step explanation:

Given

(n + 1) + 3 (n - 1) = 2 (n - 1) (n + 1) ← distribute parenthesis on both sides

n + 1 + 3n - 3 = 2 (n² - 1), that is

4n - 2 = 2n² - 2 (subtract 4n - 2 from both sides)

0 = 2n² - 4n ← factor out 2n from each term)

0 = 2n (n - 2)

Equate each factor to zero and solve for n

2n = 0 ⇒ n = 0

n - 2 = 0 ⇒ n = 2