Solve 5sqrt{3}+10+frac{sqrt{3}}{3}y=sqrt{3}(y-5)

$$5 \sqrt { 3 } + 10 + \frac { \sqrt { 3 } } { 3 } y = \sqrt { 3 } ( y - 5 )$$

Solve for y

$$y=5\sqrt{3}+15\approx 23.660254038$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$15\sqrt{3}+30+\sqrt{3}y=3\sqrt{3}\left(y-5\right)$$

Use the distributive property to multiply 3\sqrt{3} by y-5.

$$15\sqrt{3}+30+\sqrt{3}y=3\sqrt{3}y-15\sqrt{3}$$

Subtract 3\sqrt{3}y from both sides.

$$15\sqrt{3}+30+\sqrt{3}y-3\sqrt{3}y=-15\sqrt{3}$$

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

$$15\sqrt{3}+30-2\sqrt{3}y=-15\sqrt{3}$$

Subtract 15\sqrt{3} from both sides.

$$30-2\sqrt{3}y=-15\sqrt{3}-15\sqrt{3}$$

Combine -15\sqrt{3} and -15\sqrt{3} to get -30\sqrt{3}.

$$30-2\sqrt{3}y=-30\sqrt{3}$$

Subtract 30 from both sides.

$$-2\sqrt{3}y=-30\sqrt{3}-30$$

The equation is in standard form.

$$\left(-2\sqrt{3}\right)y=-30\sqrt{3}-30$$

Divide both sides by -2\sqrt{3}.

$$\frac{\left(-2\sqrt{3}\right)y}{-2\sqrt{3}}=\frac{-30\sqrt{3}-30}{-2\sqrt{3}}$$

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

$$y=\frac{-30\sqrt{3}-30}{-2\sqrt{3}}$$

Divide -30\sqrt{3}-30 by -2\sqrt{3}.

$$y=5\sqrt{3}+15$$