Solve for \( x \) \( 6 x^{3}-5 x^{2}-3 x+2=0 \) \( x=\frac{[?]}{[]}, \frac{[]}{\square]},[\square \) Enter the smallest answer first.

To solve the cubic equation \( 6x^3 - 5x^2 - 3x + 2 = 0 \), we can use methods such as synthetic division or the Rational Root Theorem to find potential rational roots. Testing possible rational roots, we discover that \( x = \frac{1}{3} \) is a solution. After factoring out \( (x - \frac{1}{3}) \), we can rewrite the equation and find the other roots. The complete solutions are \( x = \frac{2}{3}, -1, \) and \( \frac{1}{2} \). Arranging the solutions from smallest to largest, we have: \( x = -1, \frac{1}{2}, \frac{2}{3}\) Thus, the final answer is: \( x = [-1, \frac{1}{2}, \frac{2}{3}] \)