Solve c=p+1/2*rho*v^2+rho*g*h

$$c = p + \frac { 1 } { 2 } \cdot \rho \cdot v ^ { 2 } + \rho \cdot g \cdot h$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{2p+\rho v^{2}-2c}{2h\rho }\text{, }&h\neq 0\text{ and }\rho \neq 0\\g\in \mathrm{R}\text{, }&\left(c=\frac{\rho v^{2}}{2}+p\text{ and }h=0\right)\text{ or }\left(c=p\text{ and }\rho =0\text{ and }h\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$p+\frac{1}{2}\rho v^{2}+\rho gh=c$$

Subtract p from both sides.

$$\frac{1}{2}\rho v^{2}+\rho gh=c-p$$

Subtract \frac{1}{2}\rho v^{2} from both sides.

$$\rho gh=c-p-\frac{1}{2}\rho v^{2}$$

The equation is in standard form.

$$h\rho g=-\frac{\rho v^{2}}{2}+c-p$$

Divide both sides by \rho h.

$$\frac{h\rho g}{h\rho }=\frac{-\frac{\rho v^{2}}{2}+c-p}{h\rho }$$

Dividing by \rho h undoes the multiplication by \rho h.

$$g=\frac{-\frac{\rho v^{2}}{2}+c-p}{h\rho }$$

Divide c-p-\frac{v^{2}\rho }{2} by \rho h.

$$g=\frac{2c-\rho v^{2}-2p}{2h\rho }$$

Solve for c

$$c=\frac{\rho v^{2}}{2}+gh\rho +p$$