Solve A=1/2{b+(b+2zy)}*y

$$A = \frac { 1 } { 2 } \{ b + ( b + 2 z y ) \} \times y$$

Solve for b

$$\left\{\begin{matrix}b=-yz+\frac{A}{y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&A=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine b and b to get 2b.

$$A=\frac{1}{2}\left(2b+2zy\right)y$$

Use the distributive property to multiply \frac{1}{2} by 2b+2zy.

$$A=\left(b+yz\right)y$$

Use the distributive property to multiply b+yz by y.

$$A=by+zy^{2}$$

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

$$by+zy^{2}=A$$

Subtract zy^{2} from both sides.

$$by=A-zy^{2}$$

Reorder the terms.

$$by=-zy^{2}+A$$

The equation is in standard form.

$$yb=A-zy^{2}$$

Divide both sides by y.

$$\frac{yb}{y}=\frac{A-zy^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$b=\frac{A-zy^{2}}{y}$$

Divide A-zy^{2} by y.

$$b=-yz+\frac{A}{y}$$

Solve for A

$$A=y\left(yz+b\right)$$