Solve H=KV^2+BV^2

$$H = K V ^ { 2 } + B V ^ { 2 }$$

Solve for B

$$\left\{\begin{matrix}B=-K+\frac{H}{V^{2}}\text{, }&V\neq 0\\B\in \mathrm{R}\text{, }&H=0\text{ and }V=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$KV^{2}+BV^{2}=H$$

Subtract KV^{2} from both sides.

$$BV^{2}=H-KV^{2}$$

The equation is in standard form.

$$V^{2}B=H-KV^{2}$$

Divide both sides by V^{2}.

$$\frac{V^{2}B}{V^{2}}=\frac{H-KV^{2}}{V^{2}}$$

Dividing by V^{2} undoes the multiplication by V^{2}.

$$B=\frac{H-KV^{2}}{V^{2}}$$

Divide -KV^{2}+H by V^{2}.

$$B=-K+\frac{H}{V^{2}}$$

Solve for H

$$H=\left(B+K\right)V^{2}$$