Solve 2r+2pirθ/36q=50

$$2 r + \frac { 2 \pi r \theta } { 36 q } = 50$$

Solve for q

$$\left\{\begin{matrix}q=-\frac{\pi r\theta }{36\left(r-25\right)}\text{, }&\theta \neq 0\text{ and }r\neq 0\text{ and }r\neq 25\\q\neq 0\text{, }&r=25\text{ and }\theta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable q cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 36q.

$$2r\times 36q+2\pi r\theta =1800q$$

Multiply 2 and 36 to get 72.

$$72rq+2\pi r\theta =1800q$$

Subtract 1800q from both sides.

$$72rq+2\pi r\theta -1800q=0$$

Subtract 2\pi r\theta from both sides. Anything subtracted from zero gives its negation.

$$72rq-1800q=-2\pi r\theta$$

Combine all terms containing q.

$$\left(72r-1800\right)q=-2\pi r\theta$$

Divide both sides by 72r-1800.

$$\frac{\left(72r-1800\right)q}{72r-1800}=-\frac{2\pi r\theta }{72r-1800}$$

Dividing by 72r-1800 undoes the multiplication by 72r-1800.

$$q=-\frac{2\pi r\theta }{72r-1800}$$

Divide -2\pi r\theta by 72r-1800.

$$q=-\frac{\pi r\theta }{36\left(r-25\right)}$$

Variable q cannot be equal to 0.

$$q=-\frac{\pi r\theta }{36\left(r-25\right)}\text{, }q\neq 0$$

Solve for r

$$r=\frac{900q}{36q+\pi \theta }$$

$$\theta \neq -\frac{36q}{\pi }\text{ and }q\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36q.

$$2r\times 36q+2\pi r\theta =1800q$$

Multiply 2 and 36 to get 72.

$$72rq+2\pi r\theta =1800q$$

Combine all terms containing r.

$$\left(72q+2\pi \theta \right)r=1800q$$

Divide both sides by 72q+2\pi \theta .

$$\frac{\left(72q+2\pi \theta \right)r}{72q+2\pi \theta }=\frac{1800q}{72q+2\pi \theta }$$

Dividing by 72q+2\pi \theta undoes the multiplication by 72q+2\pi \theta .

$$r=\frac{1800q}{72q+2\pi \theta }$$

Divide 1800q by 72q+2\pi \theta .

$$r=\frac{900q}{36q+\pi \theta }$$