Solve y=1/4ux+3y^5

$$y = \frac { 1 } { 4 } u x + 3 y ^ { 5 }$$

Solve for u

$$\left\{\begin{matrix}u=-\frac{4y\left(3y^{4}-1\right)}{x}\text{, }&x\neq 0\\u\in \mathrm{R}\text{, }&\left(y=0\text{ or }|y|=\frac{3^{\frac{3}{4}}}{3}\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{4}ux+3y^{5}=y$$

Subtract 3y^{5} from both sides.

$$\frac{1}{4}ux=y-3y^{5}$$

The equation is in standard form.

$$\frac{x}{4}u=y-3y^{5}$$

Divide both sides by \frac{1}{4}x.

$$\frac{4\times \frac{x}{4}u}{x}=\frac{4\left(y-3y^{5}\right)}{x}$$

Dividing by \frac{1}{4}x undoes the multiplication by \frac{1}{4}x.

$$u=\frac{4\left(y-3y^{5}\right)}{x}$$

Divide y-3y^{5} by \frac{1}{4}x.

$$u=\frac{4y\left(1-3y^{4}\right)}{x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{4y\left(3y^{4}-1\right)}{u}\text{, }&u\neq 0\\x\in \mathrm{R}\text{, }&\left(y=0\text{ or }|y|=\frac{3^{\frac{3}{4}}}{3}\right)\text{ and }u=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{4}ux+3y^{5}=y$$

Subtract 3y^{5} from both sides.

$$\frac{1}{4}ux=y-3y^{5}$$

The equation is in standard form.

$$\frac{u}{4}x=y-3y^{5}$$

Divide both sides by \frac{1}{4}u.

$$\frac{4\times \frac{u}{4}x}{u}=\frac{4\left(y-3y^{5}\right)}{u}$$

Dividing by \frac{1}{4}u undoes the multiplication by \frac{1}{4}u.

$$x=\frac{4\left(y-3y^{5}\right)}{u}$$

Divide y-3y^{5} by \frac{1}{4}u.

$$x=\frac{4y\left(1-3y^{4}\right)}{u}$$