Solve 2alpha=5pirad/12+3pii/20rad

$$2 \alpha = \frac { 5 \pi r a d } { 12 } + \frac { 3 \pi i } { 20 } r a d$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\left(\frac{1500}{353}-\frac{540}{353}i\right)\alpha }{\pi dr}\text{, }&r\neq 0\text{ and }d\neq 0\\a\in \mathrm{C}\text{, }&\left(d=0\text{ or }r=0\right)\text{ and }\alpha =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 12,20.

$$120\alpha =5\times 5\pi rad+3\times 3\pi irad$$

Do the multiplications.

$$120\alpha =25\pi rad+9\pi irad$$

Multiply 9 and i to get 9i.

$$120\alpha =25\pi rad+9i\pi rad$$

Combine 25\pi rad and 9i\pi rad to get \left(25+9i\right)\pi rad.

$$120\alpha =\left(25+9i\right)\pi rad$$

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

$$\left(25+9i\right)\pi rad=120\alpha$$

The equation is in standard form.

$$\pi \left(25+9i\right)dra=120\alpha$$

Divide both sides by \left(25+9i\right)\pi rd.

$$\frac{\pi \left(25+9i\right)dra}{\pi \left(25+9i\right)dr}=\frac{120\alpha }{\pi \left(25+9i\right)dr}$$

Dividing by \left(25+9i\right)\pi rd undoes the multiplication by \left(25+9i\right)\pi rd.

$$a=\frac{120\alpha }{\pi \left(25+9i\right)dr}$$

Divide 120\alpha by \left(25+9i\right)\pi rd.

$$a=\frac{\left(\frac{1500}{353}-\frac{540}{353}i\right)\alpha }{\pi dr}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{\left(\frac{1500}{353}-\frac{540}{353}i\right)\alpha }{\pi ar}\text{, }&a\neq 0\text{ and }r\neq 0\\d\in \mathrm{C}\text{, }&\left(r=0\text{ or }a=0\right)\text{ and }\alpha =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 12,20.

$$120\alpha =5\times 5\pi rad+3\times 3\pi irad$$

Do the multiplications.

$$120\alpha =25\pi rad+9\pi irad$$

Multiply 9 and i to get 9i.

$$120\alpha =25\pi rad+9i\pi rad$$

Combine 25\pi rad and 9i\pi rad to get \left(25+9i\right)\pi rad.

$$120\alpha =\left(25+9i\right)\pi rad$$

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

$$\left(25+9i\right)\pi rad=120\alpha$$

The equation is in standard form.

$$\pi \left(25+9i\right)ard=120\alpha$$

Divide both sides by \left(25+9i\right)\pi ra.

$$\frac{\pi \left(25+9i\right)ard}{\pi \left(25+9i\right)ar}=\frac{120\alpha }{\pi \left(25+9i\right)ar}$$

Dividing by \left(25+9i\right)\pi ra undoes the multiplication by \left(25+9i\right)\pi ra.

$$d=\frac{120\alpha }{\pi \left(25+9i\right)ar}$$

Divide 120\alpha by \left(25+9i\right)\pi ra.

$$d=\frac{\left(\frac{1500}{353}-\frac{540}{353}i\right)\alpha }{\pi ar}$$