Solve d=t(v+at/2)

$$d = t ( v + \frac { a t } { 2 } )$$

Solve for a

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

Steps for Solving Linear Equation

Use the distributive property to multiply t by v+\frac{at}{2}.

$$d=tv+t\times \frac{at}{2}$$

Express t\times \frac{at}{2} as a single fraction.

$$d=tv+\frac{tat}{2}$$

Multiply t and t to get t^{2}.

$$d=tv+\frac{t^{2}a}{2}$$

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

$$tv+\frac{t^{2}a}{2}=d$$

Subtract tv from both sides.

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

Multiply both sides of the equation by 2.

$$t^{2}a=2d-2tv$$

Divide both sides by t^{2}.

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

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

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

Divide 2d-2tv by t^{2}.

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

Solve for d

$$d=\frac{t\left(at+2v\right)}{2}$$