Solve r(a^2)9*(0.3^pi/a-pi)=y

$$r ( a ^ { 2 } ) 9 \times ( \frac { 0.3 ^ { \pi } } { a } - \pi ) = y$$

Solve for r (complex solution)

$$\left\{\begin{matrix}r=\frac{y}{9a\left(0.3^{\pi }-\pi a\right)}\text{, }&a\neq 0\text{ and }a\neq \frac{0.3^{\pi }}{\pi }\\r\in \mathrm{C}\text{, }&a=\frac{0.3^{\pi }}{\pi }\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$ra^{2}\times 9\left(\frac{0.3^{\pi }}{a}-\pi \right)a=ya$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$ra^{3}\times 9\left(\frac{0.3^{\pi }}{a}-\pi \right)=ya$$

Use the distributive property to multiply ra^{3}\times 9 by \frac{0.3^{\pi }}{a}-\pi .

$$9ra^{3}\times \frac{0.3^{\pi }}{a}-9ra^{3}\pi =ya$$

Multiply both sides of the equation by a.

$$9ra^{3}\times 0.3^{\pi }-9ra^{3}\pi a=yaa$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$9ra^{3}\times 0.3^{\pi }-9ra^{4}\pi =yaa$$

Multiply a and a to get a^{2}.

$$9ra^{3}\times 0.3^{\pi }-9ra^{4}\pi =ya^{2}$$

Combine all terms containing r.

$$\left(9a^{3}\times 0.3^{\pi }-9a^{4}\pi \right)r=ya^{2}$$

The equation is in standard form.

$$\left(9\times 0.3^{\pi }a^{3}-9\pi a^{4}\right)r=ya^{2}$$

Divide both sides by 9a^{3}\times 0.3^{\pi }-9a^{4}\pi .

$$\frac{\left(9\times 0.3^{\pi }a^{3}-9\pi a^{4}\right)r}{9\times 0.3^{\pi }a^{3}-9\pi a^{4}}=\frac{ya^{2}}{9\times 0.3^{\pi }a^{3}-9\pi a^{4}}$$

Dividing by 9a^{3}\times 0.3^{\pi }-9a^{4}\pi undoes the multiplication by 9a^{3}\times 0.3^{\pi }-9a^{4}\pi .

$$r=\frac{ya^{2}}{9\times 0.3^{\pi }a^{3}-9\pi a^{4}}$$

Divide ya^{2} by 9a^{3}\times 0.3^{\pi }-9a^{4}\pi .

$$r=\frac{y}{9a\left(0.3^{\pi }-\pi a\right)}$$

Solve for r

$$\left\{\begin{matrix}r=\frac{10^{\pi }y}{9a\left(3^{\pi }-\pi \times 10^{\pi }a\right)}\text{, }&a\neq 0\text{ and }a\neq \frac{0.3^{\pi }}{\pi }\\r\in \mathrm{R}\text{, }&a=\frac{0.3^{\pi }}{\pi }\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$ra^{2}\times 9\left(\frac{0.3^{\pi }}{a}-\pi \right)a=ya$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$ra^{3}\times 9\left(\frac{0.3^{\pi }}{a}-\pi \right)=ya$$

Use the distributive property to multiply ra^{3}\times 9 by \frac{0.3^{\pi }}{a}-\pi .

$$9ra^{3}\times \frac{0.3^{\pi }}{a}-9ra^{3}\pi =ya$$

Multiply both sides of the equation by a.

$$9ra^{3}\times 0.3^{\pi }-9ra^{3}\pi a=yaa$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$9ra^{3}\times 0.3^{\pi }-9ra^{4}\pi =yaa$$

Multiply a and a to get a^{2}.

$$9ra^{3}\times 0.3^{\pi }-9ra^{4}\pi =ya^{2}$$

Combine all terms containing r.

$$\left(9a^{3}\times 0.3^{\pi }-9a^{4}\pi \right)r=ya^{2}$$

The equation is in standard form.

$$\left(9\times 0.3^{\pi }a^{3}-9\pi a^{4}\right)r=ya^{2}$$

Divide both sides by 9a^{3}\times 0.3^{\pi }-9a^{4}\pi .

$$\frac{\left(9\times 0.3^{\pi }a^{3}-9\pi a^{4}\right)r}{9\times 0.3^{\pi }a^{3}-9\pi a^{4}}=\frac{ya^{2}}{9\times 0.3^{\pi }a^{3}-9\pi a^{4}}$$

Dividing by 9a^{3}\times 0.3^{\pi }-9a^{4}\pi undoes the multiplication by 9a^{3}\times 0.3^{\pi }-9a^{4}\pi .

$$r=\frac{ya^{2}}{9\times 0.3^{\pi }a^{3}-9\pi a^{4}}$$

Divide ya^{2} by 9a^{3}\times 0.3^{\pi }-9a^{4}\pi .

$$r=\frac{10^{\pi }y}{9a\left(3^{\pi }-\pi \times 10^{\pi }a\right)}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a\neq 0\text{, }&\text{unconditionally}\\a=\frac{\sqrt{r\left(9\times 0.09^{\pi }r-4\pi y\right)}+3\times 0.3^{\pi }r}{6\pi r}\text{, }&\left(|\frac{arg(r^{2})}{2}-arg(-r)|\geq \pi \text{ or }y\neq 0\right)\text{ and }r\neq 0\\a=-\frac{\sqrt{r\left(9\times 0.09^{\pi }r-4\pi y\right)}-3\times 0.3^{\pi }r}{6\pi r}\text{, }&\left(|\frac{arg(r^{2})}{2}-arg(r)|\geq \pi \text{ or }y\neq 0\right)\text{ and }r\neq 0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}\\a\neq 0\text{, }&\text{unconditionally}\\a=\frac{\sqrt{r\left(9\times 0.09^{\pi }r-4\pi y\right)}+3\times 0.3^{\pi }r}{6\pi r}\text{, }&\left(y\neq 0\text{ and }r\leq \frac{4\pi \times \frac{100}{9}^{\pi }y}{9}\text{ and }r<0\right)\text{ or }\left(r=\frac{4\pi \times \frac{100}{9}^{\pi }y}{9}\text{ and }y\neq 0\right)\text{ or }\left(r>0\text{ and }r\geq \frac{4\pi \times \frac{100}{9}^{\pi }y}{9}\right)\\a=-\frac{\sqrt{r\left(9\times 0.09^{\pi }r-4\pi y\right)}-3\times 0.3^{\pi }r}{6\pi r}\text{, }&\left(y\neq 0\text{ and }r\geq \frac{4\pi \times \frac{100}{9}^{\pi }y}{9}\text{ and }r>0\right)\text{ or }\left(r=\frac{4\pi \times \frac{100}{9}^{\pi }y}{9}\text{ and }y\neq 0\right)\text{ or }\left(r<0\text{ and }r\leq \frac{4\pi \times \frac{100}{9}^{\pi }y}{9}\right)\end{matrix}\right.$$