Solve V=a^3-1/3a^2H

$$V = a ^ { 3 } - \frac { 1 } { 3 } a ^ { 2 } H$$

Solve for H

$$\left\{\begin{matrix}H=3a-\frac{3V}{a^{2}}\text{, }&a\neq 0\\H\in \mathrm{R}\text{, }&V=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a^{3}-\frac{1}{3}a^{2}H=V$$

Subtract a^{3} from both sides.

$$-\frac{1}{3}a^{2}H=V-a^{3}$$

The equation is in standard form.

$$\left(-\frac{a^{2}}{3}\right)H=V-a^{3}$$

Divide both sides by -\frac{1}{3}a^{2}.

$$\frac{\left(-\frac{a^{2}}{3}\right)H}{-\frac{a^{2}}{3}}=\frac{V-a^{3}}{-\frac{a^{2}}{3}}$$

Dividing by -\frac{1}{3}a^{2} undoes the multiplication by -\frac{1}{3}a^{2}.

$$H=\frac{V-a^{3}}{-\frac{a^{2}}{3}}$$

Divide -a^{3}+V by -\frac{1}{3}a^{2}.

$$H=3a-\frac{3V}{a^{2}}$$

Solve for V

$$V=-\frac{\left(H-3a\right)a^{2}}{3}$$