Solve 4+2sqrt{3}+2sqrt{3}+3=9+bsqrt{3}

$$4 + 2 \sqrt { 3 } + 2 \sqrt { 3 } + 3 = 9 + b \sqrt { 3 }$$

Solve for b

$$b=-\frac{2\sqrt{3}}{3}+4\approx 2.845299462$$

Steps for Solving Linear Equation

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

$$4+4\sqrt{3}+3=9+b\sqrt{3}$$

Add 4 and 3 to get 7.

$$7+4\sqrt{3}=9+b\sqrt{3}$$

Swap sides so that all variable terms are on the left hand side.

$$9+b\sqrt{3}=7+4\sqrt{3}$$

Subtract 9 from both sides.

$$b\sqrt{3}=7+4\sqrt{3}-9$$

Subtract 9 from 7 to get -2.

$$b\sqrt{3}=-2+4\sqrt{3}$$

The equation is in standard form.

$$\sqrt{3}b=4\sqrt{3}-2$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}b}{\sqrt{3}}=\frac{4\sqrt{3}-2}{\sqrt{3}}$$

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

$$b=\frac{4\sqrt{3}-2}{\sqrt{3}}$$

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

$$b=-\frac{2\sqrt{3}}{3}+4$$