Solve x=a(θ-sinθ)

$$x = a ( \theta - \sin \theta )$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x}{-\sin(\theta )+\theta }\text{, }&-\sin(\theta )+\theta \neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }-\sin(\theta )+\theta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a\left(\theta -\sin(\theta )\right)=x$$

Use the distributive property to multiply a by \theta -\sin(\theta ).

$$a\theta -a\sin(\theta )=x$$

Combine all terms containing a.

$$\left(\theta -\sin(\theta )\right)a=x$$

The equation is in standard form.

$$\left(-\sin(\theta )+\theta \right)a=x$$

Divide both sides by \theta -\sin(\theta ).

$$\frac{\left(-\sin(\theta )+\theta \right)a}{-\sin(\theta )+\theta }=\frac{x}{-\sin(\theta )+\theta }$$

Dividing by \theta -\sin(\theta ) undoes the multiplication by \theta -\sin(\theta ).

$$a=\frac{x}{-\sin(\theta )+\theta }$$

Solve for x

$$x=a\left(-\sin(\theta )+\theta \right)$$