Solve V=Y(r+B)

$$V = Y ( r + B )$$

Solve for B

$$\left\{\begin{matrix}B=-r+\frac{V}{Y}\text{, }&Y\neq 0\\B\in \mathrm{R}\text{, }&V=0\text{ and }Y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply Y by r+B.

$$V=Yr+YB$$

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

$$Yr+YB=V$$

Subtract Yr from both sides.

$$YB=V-Yr$$

Divide both sides by Y.

$$\frac{YB}{Y}=\frac{V-Yr}{Y}$$

Dividing by Y undoes the multiplication by Y.

$$B=\frac{V-Yr}{Y}$$

Divide V-rY by Y.

$$B=-r+\frac{V}{Y}$$

Solve for V

$$V=Y\left(r+B\right)$$