8 + 6t - 3t + t = 12t³
8 + 3t + t = 12t³
8 + 4t = 12t³
-12t³ + 4t + 8 = 0
-4(3t³) - 4(t) - 4(2) = 0
-4(3t³ - t - 2) = 0
-4 -4
3t³ - t - 2 = 0
3t³ + 3t² - 3t² + 2t - 3t - 2 = 0
3t³ + 3t² + 2t - 3t² - 3t - 2 = 0
t(3t²) + t(3t) + t(2) - 1(3t²) - 1(3t) - 1(2) = 0
t(3t² + 3t + 2) - 1(3t² + 3t + 2) = 0
(t - 1)(3t² + 3t + 2) = 0
t - 1 = 0 or 3t² + 3t + 2 = 0
+ 1 + 1 t = -(3) ± √((-3)² - 4(3)(2))
t = 1 2(3)
t = -3 ± √(9 - 24)
6
t = -3 ± √(-15)
6
t = -3 ± i√(15)
6
t = ⁻¹/₂ ± ¹/₆i√(15)
t = ⁻¹/₂ + ¹/₆i√(15) or t = ⁻¹/₂ - ¹/₆i√(15)
Solution Set: {1, ⁻¹/₂ ± ¹/₆i√(15)}
