Solve 2x{left(-frac{sqrt{6}}{3}+1/2right)}^3-3{left(frac{sqrt{3}}{6}+1/2right)}^2--frac{sqrt{6}}{3}+1/2-8

$$2x { \left(- \frac{ \sqrt{ 6 } }{ 3 } + \frac{ 1 }{ 2 } \right) }^{ 3 } -3 { \left( \frac{ \sqrt{ 3 } }{ 6 } + \frac{ 1 }{ 2 } \right) }^{ 2 } -- \frac{ \sqrt{ 6 } }{ 3 } + \frac{ 1 }{ 2 } -8$$

Factor

$$\frac{\left(81-34\sqrt{6}\right)x+12\sqrt{6}-18\sqrt{3}-306}{36}$$

Solution Steps

Factor out \frac{1}{108}.

$$\frac{x\left(-2\sqrt{6}+3\right)^{3}-9\left(\sqrt{3}+3\right)^{2}+36\sqrt{6}-810}{108}$$

Evaluate

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