Solve s=vt-1/2at^2

$$s = v t - 1 / 2 a t ^ { 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{2\left(tv-s\right)}{t^{2}}\text{, }&t\neq 0\\a\in \mathrm{C}\text{, }&s=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$vt-\frac{1}{2}at^{2}=s$$

Subtract vt from both sides.

$$-\frac{1}{2}at^{2}=s-vt$$

The equation is in standard form.

$$\left(-\frac{t^{2}}{2}\right)a=s-tv$$

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

$$\frac{\left(-\frac{t^{2}}{2}\right)a}{-\frac{t^{2}}{2}}=\frac{s-tv}{-\frac{t^{2}}{2}}$$

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

$$a=\frac{s-tv}{-\frac{t^{2}}{2}}$$

Divide s-vt by -\frac{1}{2}t^{2}.

$$a=-\frac{2\left(s-tv\right)}{t^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{2\left(tv-s\right)}{t^{2}}\text{, }&t\neq 0\\a\in \mathrm{R}\text{, }&s=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$vt-\frac{1}{2}at^{2}=s$$

Subtract vt from both sides.

$$-\frac{1}{2}at^{2}=s-vt$$

The equation is in standard form.

$$\left(-\frac{t^{2}}{2}\right)a=s-tv$$

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

$$\frac{\left(-\frac{t^{2}}{2}\right)a}{-\frac{t^{2}}{2}}=\frac{s-tv}{-\frac{t^{2}}{2}}$$

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

$$a=\frac{s-tv}{-\frac{t^{2}}{2}}$$

Divide s-tv by -\frac{1}{2}t^{2}.

$$a=-\frac{2\left(s-tv\right)}{t^{2}}$$

Solve for s

$$s=-\frac{t\left(at-2v\right)}{2}$$