Solve Q=-xr+cxleft(T-tright)

$$Q = -xr+cx \left( T-t \right)$$

Solve for T

$$\left\{\begin{matrix}T=\frac{ctx+rx+Q}{cx}\text{, }&x\neq 0\text{ and }c\neq 0\\T\in \mathrm{R}\text{, }&\left(Q=0\text{ and }x=0\right)\text{ or }\left(Q=-rx\text{ and }c=0\text{ and }x\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply cx by T-t.

$$Q=\left(-x\right)r+cxT-cxt$$

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

$$\left(-x\right)r+cxT-cxt=Q$$

Subtract \left(-x\right)r from both sides.

$$cxT-cxt=Q-\left(-x\right)r$$

Add cxt to both sides.

$$cxT=Q-\left(-x\right)r+cxt$$

Multiply -1 and -1 to get 1.

$$cxT=Q+xr+cxt$$

The equation is in standard form.

$$cxT=ctx+rx+Q$$

Divide both sides by cx.

$$\frac{cxT}{cx}=\frac{ctx+rx+Q}{cx}$$

Dividing by cx undoes the multiplication by cx.

$$T=\frac{ctx+rx+Q}{cx}$$

Divide Q+xr+cxt by cx.

$$T=t+\frac{rx+Q}{cx}$$

Solve for Q

$$Q=x\left(c\left(T-t\right)-r\right)$$