log₃(x - 2) + log₃(x + 6) = 2
log₃((x - 2)(x + 6)) = 2
log₃(x(x + 6) - 2(x + 6)) = 2
log₃(x(x) + x(6) - 2(x) - 2(6)) = 2
log₃(x² + 6x - 2x - 12) = 2
log₃(x² + 4x - 12) = 2
3² = x² + 4x - 12
9 = x² + 4x - 12
- 9 - 9
0 = x² + 4x - 21
0 = x² + 7x - 3x - 21
0 = x(x) + x(7) - 3(x) - 3(7)
0 = x(x + 7) - 3(x + 7)
0 = (x - 3)(x + 7)
0 = x - 3 or 0 = x + 7
+ 3 + 3 - 7 - 7
3 = x or -7 = x