Solve Q=k*A*(T_{2}-T_{1})

$$Q = k \cdot A \cdot ( T _ { 2 } - T _ { 1 } )$$

Solve for A

$$\left\{\begin{matrix}A=\frac{Q}{k\left(T_{2}-T_{1}\right)}\text{, }&T_{2}\neq T_{1}\text{ and }k\neq 0\\A\in \mathrm{R}\text{, }&\left(T_{2}=T_{1}\text{ or }k=0\right)\text{ and }Q=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply kA by T_{2}-T_{1}.

$$Q=kAT_{2}-kAT_{1}$$

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

$$kAT_{2}-kAT_{1}=Q$$

Combine all terms containing A.

$$\left(kT_{2}-kT_{1}\right)A=Q$$

The equation is in standard form.

$$\left(T_{2}k-T_{1}k\right)A=Q$$

Divide both sides by -T_{1}k+T_{2}k.

$$\frac{\left(T_{2}k-T_{1}k\right)A}{T_{2}k-T_{1}k}=\frac{Q}{T_{2}k-T_{1}k}$$

Dividing by -T_{1}k+T_{2}k undoes the multiplication by -T_{1}k+T_{2}k.

$$A=\frac{Q}{T_{2}k-T_{1}k}$$

Divide Q by -T_{1}k+T_{2}k.

$$A=\frac{Q}{k\left(T_{2}-T_{1}\right)}$$

Solve for Q

$$Q=Ak\left(T_{2}-T_{1}\right)$$