To solve this cubic equation, we can try factoring by grouping or using the rational root theorem. Let's first try factoring by grouping:
2x^3 - 4x^2 - 3x + 6 = 02x^2(x - 2) - 3(x - 2) = 0(2x^2 - 3)(x - 2) = 0.
Setting each factor to zero gives us:
2x^2 - 3 = 0 and x - 2 = 02x^2 = 3 and x = 2x^2 = 3/2x = ±√(3/2).
Therefore, the solutions to the equation 2x^3 - 4x^2 - 3x + 6 = 0 are x = √(3/2), x = -√(3/2), and x = 2.
To solve this cubic equation, we can try factoring by grouping or using the rational root theorem. Let's first try factoring by grouping:
2x^3 - 4x^2 - 3x + 6 = 0
2x^2(x - 2) - 3(x - 2) = 0
(2x^2 - 3)(x - 2) = 0.
Setting each factor to zero gives us:
2x^2 - 3 = 0 and x - 2 = 0
2x^2 = 3 and x = 2
x^2 = 3/2
x = ±√(3/2).
Therefore, the solutions to the equation 2x^3 - 4x^2 - 3x + 6 = 0 are x = √(3/2), x = -√(3/2), and x = 2.