Solve A=2(ab+ac+bc)

$$A = 2 ( a b + a c + b c )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{2bc-A}{2\left(b+c\right)}\text{, }&b\neq -c\\a\in \mathrm{C}\text{, }&A=-2b^{2}\text{ and }c=-b\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by ab+ac+bc.

$$A=2ab+2ac+2bc$$

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

$$2ab+2ac+2bc=A$$

Subtract 2bc from both sides.

$$2ab+2ac=A-2bc$$

Combine all terms containing a.

$$\left(2b+2c\right)a=A-2bc$$

Divide both sides by 2b+2c.

$$\frac{\left(2b+2c\right)a}{2b+2c}=\frac{A-2bc}{2b+2c}$$

Dividing by 2b+2c undoes the multiplication by 2b+2c.

$$a=\frac{A-2bc}{2b+2c}$$

Divide A-2cb by 2b+2c.

$$a=\frac{A-2bc}{2\left(b+c\right)}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{2bc-A}{2\left(b+c\right)}\text{, }&b\neq -c\\a\in \mathrm{R}\text{, }&A=-2b^{2}\text{ and }c=-b\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by ab+ac+bc.

$$A=2ab+2ac+2bc$$

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

$$2ab+2ac+2bc=A$$

Subtract 2bc from both sides.

$$2ab+2ac=A-2bc$$

Combine all terms containing a.

$$\left(2b+2c\right)a=A-2bc$$

Divide both sides by 2b+2c.

$$\frac{\left(2b+2c\right)a}{2b+2c}=\frac{A-2bc}{2b+2c}$$

Dividing by 2b+2c undoes the multiplication by 2b+2c.

$$a=\frac{A-2bc}{2b+2c}$$

Divide A-2cb by 2b+2c.

$$a=\frac{A-2bc}{2\left(b+c\right)}$$

Solve for A

$$A=2\left(ab+ac+bc\right)$$