Solve {l}{2x(-frac{sqrt{6}}{3}+1/2)^3-3(frac{sqrt{3}}{6}+1/2)^2}{-+(-frac{sqrt{6}}{3}+1/2)-b}

$$\left. \begin{array} { l } { 2 x ( - \frac { \sqrt { 6 } } { 3 } + \frac { 1 } { 2 } ) ^ { 3 } - 3 ( \frac { \sqrt { 3 } } { 6 } + \frac { 1 } { 2 } ) ^ { 2 } } \\ { - + ( - \frac { \sqrt { 6 } } { 3 } + \frac { 1 } { 2 } ) - b } \end{array} \right.$$

Factor

$$\frac{\left(81-34\sqrt{6}\right)x-36b+12\sqrt{6}-18\sqrt{3}-54}{36}$$

Solution Steps

Factor out \frac{1}{108}.

$$\frac{x\left(-2\sqrt{6}+3\right)^{3}-9\left(\sqrt{3}+3\right)^{2}-18\left(-2\sqrt{6}+3\right)-108b}{108}$$

Evaluate

$$-\frac{17\sqrt{6}x}{18}+\frac{9x}{4}-b+\frac{\sqrt{6}}{3}-\frac{\sqrt{3}}{2}-\frac{3}{2}$$