Solve p=xq+2x+2q+10

$$p = x q + 2 x + 2 q + 10$$

Solve for q (complex solution)

$$\left\{\begin{matrix}q=-\frac{2x-p+10}{x+2}\text{, }&x\neq -2\\q\in \mathrm{C}\text{, }&p=6\text{ and }x=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$xq+2x+2q+10=p$$

Subtract 2x from both sides.

$$xq+2q+10=p-2x$$

Subtract 10 from both sides.

$$xq+2q=p-2x-10$$

Combine all terms containing q.

$$\left(x+2\right)q=p-2x-10$$

The equation is in standard form.

$$\left(x+2\right)q=-2x+p-10$$

Divide both sides by x+2.

$$\frac{\left(x+2\right)q}{x+2}=\frac{-2x+p-10}{x+2}$$

Dividing by x+2 undoes the multiplication by x+2.

$$q=\frac{-2x+p-10}{x+2}$$

Solve for q

$$\left\{\begin{matrix}q=-\frac{2x-p+10}{x+2}\text{, }&x\neq -2\\q\in \mathrm{R}\text{, }&p=6\text{ and }x=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$xq+2x+2q+10=p$$

Subtract 2x from both sides.

$$xq+2q+10=p-2x$$

Subtract 10 from both sides.

$$xq+2q=p-2x-10$$

Combine all terms containing q.

$$\left(x+2\right)q=p-2x-10$$

The equation is in standard form.

$$\left(x+2\right)q=-2x+p-10$$

Divide both sides by x+2.

$$\frac{\left(x+2\right)q}{x+2}=\frac{-2x+p-10}{x+2}$$

Dividing by x+2 undoes the multiplication by x+2.

$$q=\frac{-2x+p-10}{x+2}$$

Solve for p

$$p=qx+2x+2q+10$$