What is the sum of the solutions to $6x^3+7x^2-x-2=0$ What is the easy way to solve the problem? 

The sum of the solutions to $6x^3+7x^2-x-2=0$ is:
  $$A) \ \frac{1}{6}$$ $$B) \ \frac{1}{3}$$ $$C) \ \frac{-7}{6}$$ $$D) -2$$ $$E) \text{ none of above}$$


We could factor the cubic polynomial as $6(x-x_1)(x-x_2)(x-x_3)$. 
Then, note that the coefficient on the quadratic term is $-6(x_1+x_2+x_3)=7$
Hence, $x_1+x_2+x_3=-\frac 76$.  
This result can be generalized for an $n$'th order polynomial and is part of Vieta's Foumulae as referenced in a comment by @Vadim123.
