Solve r=r(1+cosθ)

$$r = r ( 1 + \cos \theta )$$

Solve for r

$$\left\{\begin{matrix}\\r=0\text{, }&\text{unconditionally}\\r\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply r by 1+\cos(\theta ).

$$r=r+r\cos(\theta )$$

Subtract r from both sides.

$$r-r=r\cos(\theta )$$

Combine r and -r to get 0.

$$0=r\cos(\theta )$$

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

$$r\cos(\theta )=0$$

The equation is in standard form.

$$\cos(\theta )r=0$$

Divide 0 by \cos(\theta ).

$$r=0$$

Solve for θ

$$\left\{\begin{matrix}\\\theta =\pi n_{1}+\frac{\pi }{2}\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\\theta \in \mathrm{R}\text{, }&r=0\end{matrix}\right.$$