Solve I(nu)dnu=8pinu^2/a^3kTdnu

$$I ( \nu ) d \nu = \frac { 8 \pi \nu ^ { 2 } } { a ^ { 3 } } k T d \nu$$

Solve for I

$$\left\{\begin{matrix}I=\frac{8\pi Tk\nu }{a^{3}}\text{, }&a\neq 0\\I\in \mathrm{R}\text{, }&\left(\nu =0\text{ or }d=0\right)\text{ and }a\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a^{3}.

$$I\nu d\nu a^{3}=8\pi \nu ^{2}kTd\nu$$

Multiply \nu and \nu to get \nu ^{2}.

$$I\nu ^{2}da^{3}=8\pi \nu ^{2}kTd\nu$$

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

$$I\nu ^{2}da^{3}=8\pi \nu ^{3}kTd$$

The equation is in standard form.

$$d\nu ^{2}a^{3}I=8\pi Tdk\nu ^{3}$$

Divide both sides by \nu ^{2}da^{3}.

$$\frac{d\nu ^{2}a^{3}I}{d\nu ^{2}a^{3}}=\frac{8\pi Tdk\nu ^{3}}{d\nu ^{2}a^{3}}$$

Dividing by \nu ^{2}da^{3} undoes the multiplication by \nu ^{2}da^{3}.

$$I=\frac{8\pi Tdk\nu ^{3}}{d\nu ^{2}a^{3}}$$

Divide 8\pi \nu ^{3}kTd by \nu ^{2}da^{3}.

$$I=\frac{8\pi Tk\nu }{a^{3}}$$

Solve for T

$$\left\{\begin{matrix}T=\frac{Ia^{3}}{8\pi k\nu }\text{, }&\nu \neq 0\text{ and }k\neq 0\text{ and }a\neq 0\\T\in \mathrm{R}\text{, }&\left(d=0\text{ and }a\neq 0\right)\text{ or }\left(I=0\text{ and }k=0\text{ and }a\neq 0\right)\text{ or }\left(\nu =0\text{ and }a\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a^{3}.

$$I\nu d\nu a^{3}=8\pi \nu ^{2}kTd\nu$$

Multiply \nu and \nu to get \nu ^{2}.

$$I\nu ^{2}da^{3}=8\pi \nu ^{2}kTd\nu$$

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

$$I\nu ^{2}da^{3}=8\pi \nu ^{3}kTd$$

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

$$8\pi \nu ^{3}kTd=I\nu ^{2}da^{3}$$

The equation is in standard form.

$$8\pi dk\nu ^{3}T=Id\nu ^{2}a^{3}$$

Divide both sides by 8\pi \nu ^{3}kd.

$$\frac{8\pi dk\nu ^{3}T}{8\pi dk\nu ^{3}}=\frac{Id\nu ^{2}a^{3}}{8\pi dk\nu ^{3}}$$

Dividing by 8\pi \nu ^{3}kd undoes the multiplication by 8\pi \nu ^{3}kd.

$$T=\frac{Id\nu ^{2}a^{3}}{8\pi dk\nu ^{3}}$$

Divide I\nu ^{2}da^{3} by 8\pi \nu ^{3}kd.

$$T=\frac{Ia^{3}}{8\pi k\nu }$$