Solve sqrt{3}(x-2)-2xsqrt{2}=2(xsqrt{3}-3-xsqrt{2})

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

Solve for x

$$x=2\left(\sqrt{3}-1\right)\approx 1.464101615$$

Steps for Solving Linear Equation

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

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

Subtract 2\left(x\sqrt{3}-3-x\sqrt{2}\right) from both sides.

$$\sqrt{3}x-2\sqrt{3}-2x\sqrt{2}-2\left(x\sqrt{3}-3-x\sqrt{2}\right)=0$$

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

$$\sqrt{3}x-2\sqrt{3}-2x\sqrt{2}-2x\sqrt{3}+6+2\sqrt{2}x=0$$

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

$$-\sqrt{3}x-2\sqrt{3}-2x\sqrt{2}+6+2\sqrt{2}x=0$$

Combine -2x\sqrt{2} and 2\sqrt{2}x to get 0.

$$-\sqrt{3}x-2\sqrt{3}+6=0$$

Add 2\sqrt{3} to both sides. Anything plus zero gives itself.

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

Subtract 6 from both sides.

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

The equation is in standard form.

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

Divide both sides by -\sqrt{3}.

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

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

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

Divide 2\sqrt{3}-6 by -\sqrt{3}.

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