Solve x+2=(x-2sqrt{3})*sqrt{3}

$$x+2=(x-2 \sqrt{ 3 } ) \times \sqrt{ 3 }$$

Solve for x

$$x=4\left(\sqrt{3}+1\right)\approx 10.92820323$$

Steps for Solving Linear Equation

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

$$x+2=x\sqrt{3}-2\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

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

Multiply -2 and 3 to get -6.

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

Subtract x\sqrt{3} from both sides.

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

Subtract 2 from both sides.

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

Subtract 2 from -6 to get -8.

$$x-x\sqrt{3}=-8$$

Combine all terms containing x.

$$\left(1-\sqrt{3}\right)x=-8$$

Divide both sides by 1-\sqrt{3}.

$$\frac{\left(1-\sqrt{3}\right)x}{1-\sqrt{3}}=-\frac{8}{1-\sqrt{3}}$$

Dividing by 1-\sqrt{3} undoes the multiplication by 1-\sqrt{3}.

$$x=-\frac{8}{1-\sqrt{3}}$$

Divide -8 by 1-\sqrt{3}.

$$x=4\sqrt{3}+4$$