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

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

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

Steps for Solving Linear Equation

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

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Combine -3\sqrt{2} and 3\sqrt{2} to get 0.

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

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

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

Subtract x^{2} from both sides.

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

Combine x^{2} and -x^{2} to get 0.

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

Subtract x\sqrt{6} from both sides.

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

Combine x\sqrt{6} and -x\sqrt{6} to get 0.

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

The equation is in standard form.

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

Divide both sides by -\sqrt{3}.

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

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

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

Divide -3 by -\sqrt{3}.

$$x=\sqrt{3}$$