solv for x, 6x^3 -7x^2 -12x +7 = 0
Using the Rational Zeros Test:
f\:7}{Factors\f\:6} = \dfrac{\pm 1,\,\pm 7}{\pm 1,\,\pm 2,\,\pm 3,\,\pm 6}" alt="\dfrac{Factors\f\:7}{Factors\f\:6} = \dfrac{\pm 1,\,\pm 7}{\pm 1,\,\pm 2,\,\pm 3,\,\pm 6}" />
... and guess-and-check with these potential rational zeros, I see that 1/2 is a zero. So the polynomial factors to:
The quadratic isn't factorable, so you'll have to use the quadratic formula to get the other two roots.