Solve 4sqrt{3}(x+2)=2sqrt{3}(6+2sqrt{3}+x)

$$4 \sqrt{ 3 } (x+2)=2 \sqrt{ 3 } (6+2 \sqrt{ 3 } +x)$$

Solve for x

$$x=2\left(\sqrt{3}+1\right)\approx 5.464101615$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4\sqrt{3} by x+2.

$$4\sqrt{3}x+8\sqrt{3}=2\sqrt{3}\left(6+2\sqrt{3}+x\right)$$

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

$$4\sqrt{3}x+8\sqrt{3}=12\sqrt{3}+4\left(\sqrt{3}\right)^{2}+2\sqrt{3}x$$

The square of \sqrt{3} is 3.

$$4\sqrt{3}x+8\sqrt{3}=12\sqrt{3}+4\times 3+2\sqrt{3}x$$

Multiply 4 and 3 to get 12.

$$4\sqrt{3}x+8\sqrt{3}=12\sqrt{3}+12+2\sqrt{3}x$$

Subtract 2\sqrt{3}x from both sides.

$$4\sqrt{3}x+8\sqrt{3}-2\sqrt{3}x=12\sqrt{3}+12$$

Combine 4\sqrt{3}x and -2\sqrt{3}x to get 2\sqrt{3}x.

$$2\sqrt{3}x+8\sqrt{3}=12\sqrt{3}+12$$

Subtract 8\sqrt{3} from both sides.

$$2\sqrt{3}x=12\sqrt{3}+12-8\sqrt{3}$$

Combine 12\sqrt{3} and -8\sqrt{3} to get 4\sqrt{3}.

$$2\sqrt{3}x=4\sqrt{3}+12$$

Divide both sides by 2\sqrt{3}.

$$\frac{2\sqrt{3}x}{2\sqrt{3}}=\frac{4\sqrt{3}+12}{2\sqrt{3}}$$

Dividing by 2\sqrt{3} undoes the multiplication by 2\sqrt{3}.

$$x=\frac{4\sqrt{3}+12}{2\sqrt{3}}$$

Divide 4\sqrt{3}+12 by 2\sqrt{3}.

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