Solve n20w^3+7w^2-3w=0

$$n 20 w ^ { 3 } + 7 w ^ { 2 } - 3 w = 0$$

Solve for n_20 (complex solution)

$$\left\{\begin{matrix}n_{20}=-\frac{7w-3}{w^{2}}\text{, }&w\neq 0\\n_{20}\in \mathrm{C}\text{, }&w=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 7w^{2} from both sides. Anything subtracted from zero gives its negation.

$$n_{20}w^{3}-3w=-7w^{2}$$

Add 3w to both sides.

$$n_{20}w^{3}=-7w^{2}+3w$$

The equation is in standard form.

$$w^{3}n_{20}=3w-7w^{2}$$

Divide both sides by w^{3}.

$$\frac{w^{3}n_{20}}{w^{3}}=\frac{w\left(3-7w\right)}{w^{3}}$$

Dividing by w^{3} undoes the multiplication by w^{3}.

$$n_{20}=\frac{w\left(3-7w\right)}{w^{3}}$$

Divide w\left(3-7w\right) by w^{3}.

$$n_{20}=\frac{3-7w}{w^{2}}$$

Solve for n_20

$$\left\{\begin{matrix}n_{20}=-\frac{7w-3}{w^{2}}\text{, }&w\neq 0\\n_{20}\in \mathrm{R}\text{, }&w=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 7w^{2} from both sides. Anything subtracted from zero gives its negation.

$$n_{20}w^{3}-3w=-7w^{2}$$

Add 3w to both sides.

$$n_{20}w^{3}=-7w^{2}+3w$$

The equation is in standard form.

$$w^{3}n_{20}=3w-7w^{2}$$

Divide both sides by w^{3}.

$$\frac{w^{3}n_{20}}{w^{3}}=\frac{w\left(3-7w\right)}{w^{3}}$$

Dividing by w^{3} undoes the multiplication by w^{3}.

$$n_{20}=\frac{w\left(3-7w\right)}{w^{3}}$$

Divide w\left(3-7w\right) by w^{3}.

$$n_{20}=\frac{3-7w}{w^{2}}$$

Solve for w (complex solution)

$$\left\{\begin{matrix}\\w=0\text{, }&\text{unconditionally}\\w=\frac{\sqrt{12n_{20}+49}-7}{2n_{20}}\text{; }w=-\frac{\sqrt{12n_{20}+49}+7}{2n_{20}}\text{, }&n_{20}\neq 0\\w=\frac{3}{7}\text{, }&n_{20}=0\end{matrix}\right.$$

Solve for w

$$\left\{\begin{matrix}\\w=0\text{, }&\text{unconditionally}\\w=\frac{\sqrt{12n_{20}+49}-7}{2n_{20}}\text{; }w=-\frac{\sqrt{12n_{20}+49}+7}{2n_{20}}\text{, }&n_{20}\neq 0\text{ and }n_{20}\geq -\frac{49}{12}\\w=\frac{3}{7}\text{, }&n_{20}=0\end{matrix}\right.$$