Solve 12=V_{0}t_{2}-1/2gt_2^2=

$$12 = V _ { 0 } t _ { 2 } - \frac { 1 } { 2 } g t _ { 2 } ^ { 2 } =$$

Solve for V_0

$$V_{0}=\frac{gt_{2}}{2}+\frac{12}{t_{2}}$$

$$t_{2}\neq 0$$

Steps for Solving Linear Equation

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

$$V_{0}t_{2}-\frac{1}{2}gt_{2}^{2}=12$$

Add \frac{1}{2}gt_{2}^{2} to both sides.

$$V_{0}t_{2}=12+\frac{1}{2}gt_{2}^{2}$$

The equation is in standard form.

$$t_{2}V_{0}=\frac{gt_{2}^{2}}{2}+12$$

Divide both sides by t_{2}.

$$\frac{t_{2}V_{0}}{t_{2}}=\frac{\frac{gt_{2}^{2}}{2}+12}{t_{2}}$$

Dividing by t_{2} undoes the multiplication by t_{2}.

$$V_{0}=\frac{\frac{gt_{2}^{2}}{2}+12}{t_{2}}$$

Divide 12+\frac{gt_{2}^{2}}{2} by t_{2}.

$$V_{0}=\frac{gt_{2}}{2}+\frac{12}{t_{2}}$$

Solve for g

$$g=\frac{2\left(V_{0}t_{2}-12\right)}{t_{2}^{2}}$$

$$t_{2}\neq 0$$

Steps for Solving Linear Equation

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

$$V_{0}t_{2}-\frac{1}{2}gt_{2}^{2}=12$$

Subtract V_{0}t_{2} from both sides.

$$-\frac{1}{2}gt_{2}^{2}=12-V_{0}t_{2}$$

The equation is in standard form.

$$\left(-\frac{t_{2}^{2}}{2}\right)g=12-V_{0}t_{2}$$

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

$$\frac{\left(-\frac{t_{2}^{2}}{2}\right)g}{-\frac{t_{2}^{2}}{2}}=\frac{12-V_{0}t_{2}}{-\frac{t_{2}^{2}}{2}}$$

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

$$g=\frac{12-V_{0}t_{2}}{-\frac{t_{2}^{2}}{2}}$$

Divide 12-t_{2}V_{0} by -\frac{1}{2}t_{2}^{2}.

$$g=-\frac{2\left(12-V_{0}t_{2}\right)}{t_{2}^{2}}$$