tan³(x) + tan²(x) - 3tan(x) - 3 = 0

Factor by grouping.  

Factor tan²(x) out of the
first two terms on the left.

Factor -3 out of the
last two terms on the left.

tan²(x)[tan(x) + 1] - 3[tan(x) + 1] = 0

Factor [tan(x) + 1] out of both terms on the left:

[tan(x) + 1][tan²(x) - 3] = 0

Use the zero-factor property:

tan(x) + 1 = 0;   tan²(x) - 3 = 0

    tan(x) = -1       tan²(x) = 3

 x = ,             tan = ±√3

                      x = ,, , 

Edwin