Solve (3+sqrt{3})z+2=5+3-sqrt{3}

$$( 3 + \sqrt { 3 } ) z + 2 = 5 + 3 - \sqrt { 3 }$$

Solve for z

$$z=\frac{7-3\sqrt{3}}{2}\approx 0.901923789$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3+\sqrt{3} by z.

$$3z+\sqrt{3}z+2=5+3-\sqrt{3}$$

Add 5 and 3 to get 8.

$$3z+\sqrt{3}z+2=8-\sqrt{3}$$

Subtract 2 from both sides.

$$3z+\sqrt{3}z=8-\sqrt{3}-2$$

Subtract 2 from 8 to get 6.

$$3z+\sqrt{3}z=6-\sqrt{3}$$

Combine all terms containing z.

$$\left(3+\sqrt{3}\right)z=6-\sqrt{3}$$

The equation is in standard form.

$$\left(\sqrt{3}+3\right)z=6-\sqrt{3}$$

Divide both sides by 3+\sqrt{3}.

$$\frac{\left(\sqrt{3}+3\right)z}{\sqrt{3}+3}=\frac{6-\sqrt{3}}{\sqrt{3}+3}$$

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

$$z=\frac{6-\sqrt{3}}{\sqrt{3}+3}$$

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

$$z=\frac{7-3\sqrt{3}}{2}$$