The equation x^3-3x^2-6x+8 = 0 has to be solved for x.

x^3-3x^2-6x+8 = 0

=> x^3 - x^2 - 2x^2 + 2x - 8x + 8 = 0

=> x^2(x - 1) - 2x(x - 1) - 8(x - 1) = 0

=> (x^2 - 2x - 8)(x - 1) = 0

=> (x^2 - 4x + 2x - 8)(x - 1) = 0

=> (x(x - 4) + 2(x - 4))(x - 1) = 0

=> (x + 2)(x - 4)(x - 1) = 0

=> x = -2, x = 4 and x = 1

**The roots of the equation x^3-3x^2-6x+8 = 0 are {-2, 1, 4}**

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