Solve x=-6-2div(y-3)

$$x=-6-2 \div (y-3)$$

Solve for y

$$y=\frac{3x+16}{x+6}$$

$$x\neq -6$$

Steps for Solving Linear Equation

Variable y cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by y-3.

$$x\left(y-3\right)=\left(y-3\right)\left(-6\right)-2$$

Use the distributive property to multiply x by y-3.

$$xy-3x=\left(y-3\right)\left(-6\right)-2$$

Use the distributive property to multiply y-3 by -6.

$$xy-3x=-6y+18-2$$

Subtract 2 from 18 to get 16.

$$xy-3x=-6y+16$$

Add 6y to both sides.

$$xy-3x+6y=16$$

Add 3x to both sides.

$$xy+6y=16+3x$$

Combine all terms containing y.

$$\left(x+6\right)y=16+3x$$

The equation is in standard form.

$$\left(x+6\right)y=3x+16$$

Divide both sides by x+6.

$$\frac{\left(x+6\right)y}{x+6}=\frac{3x+16}{x+6}$$

Dividing by x+6 undoes the multiplication by x+6.

$$y=\frac{3x+16}{x+6}$$

Variable y cannot be equal to 3.

$$y=\frac{3x+16}{x+6}\text{, }y\neq 3$$

Solve for x

$$x=-\frac{2\left(3y-8\right)}{y-3}$$

$$y\neq 3$$