Solve 2sqrt{3(sqrt{6}-sqrt{2})}=xsqrt{2}-sqrt{3})*3-sqrt{3}

$$2 \sqrt { 3 ( \sqrt { 6 } - \sqrt { 2 } ) } = x \sqrt { 2 } - \sqrt { 3 } ) \cdot 3 - \sqrt { 3 }$$

Solve for x

$$x=\sqrt{6\sqrt{6}-6\sqrt{2}}+\frac{\sqrt{6}}{2}\approx 3.71706449$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by \sqrt{6}-\sqrt{2}.

$$2\sqrt{3\sqrt{6}-3\sqrt{2}}=x\sqrt{2}-\sqrt{3}$$

Swap sides so that all variable terms are on the left hand side.

$$x\sqrt{2}-\sqrt{3}=2\sqrt{3\sqrt{6}-3\sqrt{2}}$$

Add \sqrt{3} to both sides.

$$x\sqrt{2}=2\sqrt{3\sqrt{6}-3\sqrt{2}}+\sqrt{3}$$

The equation is in standard form.

$$\sqrt{2}x=2\sqrt{3\sqrt{6}-3\sqrt{2}}+\sqrt{3}$$

Divide both sides by \sqrt{2}.

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

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

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

Divide \left(2\sqrt{\sqrt{6}-\sqrt{2}}+1\right)\sqrt{3} by \sqrt{2}.

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