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

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

Solve for a

$$\left\{\begin{matrix}a=\frac{60\alpha }{17\pi dr}\text{, }&r\neq 0\text{ and }d\neq 0\\a\in \mathrm{R}\text{, }&\left(d=0\text{ or }r=0\right)\text{ and }\alpha =0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Do the multiplications.

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

Combine 25\pi rad and 9\pi rad to get 34\pi rad.

$$120\alpha =34\pi rad$$

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

$$34\pi rad=120\alpha$$

The equation is in standard form.

$$34\pi dra=120\alpha$$

Divide both sides by 34\pi rd.

$$\frac{34\pi dra}{34\pi dr}=\frac{120\alpha }{34\pi dr}$$

Dividing by 34\pi rd undoes the multiplication by 34\pi rd.

$$a=\frac{120\alpha }{34\pi dr}$$

Divide 120\alpha by 34\pi rd.

$$a=\frac{60\alpha }{17\pi dr}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{60\alpha }{17\pi ar}\text{, }&a\neq 0\text{ and }r\neq 0\\d\in \mathrm{R}\text{, }&\left(r=0\text{ or }a=0\right)\text{ and }\alpha =0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Do the multiplications.

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

Combine 25\pi rad and 9\pi rad to get 34\pi rad.

$$120\alpha =34\pi rad$$

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

$$34\pi rad=120\alpha$$

The equation is in standard form.

$$34\pi ard=120\alpha$$

Divide both sides by 34\pi ra.

$$\frac{34\pi ard}{34\pi ar}=\frac{120\alpha }{34\pi ar}$$

Dividing by 34\pi ra undoes the multiplication by 34\pi ra.

$$d=\frac{120\alpha }{34\pi ar}$$

Divide 120\alpha by 34\pi ra.

$$d=\frac{60\alpha }{17\pi ar}$$