Solve -h=left(2x-gtright)t/2

$$-h = \frac{ \left( 2x-gt \right) t }{ 2 }$$

Solve for g

$$\left\{\begin{matrix}g=\frac{2\left(tx+h\right)}{t^{2}}\text{, }&t\neq 0\\g\in \mathrm{R}\text{, }&h=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$-2h=\left(2x-gt\right)t$$

Use the distributive property to multiply 2x-gt by t.

$$-2h=2xt-gt^{2}$$

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

$$2xt-gt^{2}=-2h$$

Subtract 2xt from both sides.

$$-gt^{2}=-2h-2xt$$

The equation is in standard form.

$$\left(-t^{2}\right)g=-2tx-2h$$

Divide both sides by -t^{2}.

$$\frac{\left(-t^{2}\right)g}{-t^{2}}=\frac{-2tx-2h}{-t^{2}}$$

Dividing by -t^{2} undoes the multiplication by -t^{2}.

$$g=\frac{-2tx-2h}{-t^{2}}$$

Divide -2h-2xt by -t^{2}.

$$g=\frac{2\left(tx+h\right)}{t^{2}}$$

Solve for h

$$h=\frac{t\left(gt-2x\right)}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$-2h=\left(2x-gt\right)t$$

Use the distributive property to multiply 2x-gt by t.

$$-2h=2xt-gt^{2}$$

The equation is in standard form.

$$-2h=2tx-gt^{2}$$

Divide both sides by -2.

$$\frac{-2h}{-2}=\frac{t\left(2x-gt\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$h=\frac{t\left(2x-gt\right)}{-2}$$

Divide t\left(2x-gt\right) by -2.

$$h=-\frac{t\left(2x-gt\right)}{2}$$