how can i solve this equation and find out the values for (x).
rational root theorem, that every rational root of a polynomial with integer coefficients must be of the form where is a factor of the constant term and is a factor of the leading coefficient. The constant term in this polynomial is 6 which has factors 1, 2, 3, and 6, and the leading coefficient is also 6. That means the possible rational roots are
By testing each of these with synthetic division, we find that 2 is a root of the polynomial and hence is a factor (we can also determine that and are roots).
By the "rational root theorem" we can see that any possible rational number roots must be fractions having numerators and denominators factors of 6. A quick search for integer roots shows that 2 and -3 both satisfy the equation and so x- 2 and x+ 3 are factors. Dividing by the those leaves so that x= 1/3 and x= -1/2 are the other two roots.