12x cubbed - 9x squared + 4x-3=0

roots are ...

±i√3/3 3/4

Step-by-step explanation:

The equation can be factored by grouping:

(12x^3 - 9x^2) + (4x - 3) = 0

3x^2 (4x - 3) + (4x - 3) = 0

(3x^2 + 1) (4x - 3) = 0

The equation has roots that are the values of x making these factors zero:

3x^2 + 1 = 0

x^2 = - 1/3 = - 3/9

x = ± (i/3) √3

and

4x - 3 = 0

4x = 3

x = 3/4

The one real root is x = 3/4; the two complex roots are ±√3/3.