Answer: n = 1, n = -1/3
Step-by-step explanation:
(3n - 1)² = 12n + 8
9n² - 6n + 1 = 12n + 8
9n² - 18n - 7 = 0
Substitute -18n with 3n - 21n and find the common factor of each side:
9n² + 3n -21n - 7 = 0
3n(3n + 1) -3(3n + 1) = 0
(3n - 3) (3n + 1) = 0
Solve for each factor:
3n - 3 = 0 3n + 1 = 0
3n = 3 3n = -1
n = 1 n = -1/3
