Solve yf(x)=x^4+4x^3-16x^2-64x

$$y f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 16 x ^ { 2 } - 64 x$$

Solve for f

$$\left\{\begin{matrix}f=\frac{\left(x-4\right)\left(x+4\right)^{2}}{y}\text{, }&y\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ or }\left(y=0\text{ and }|x|=4\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xyf=x^{4}+4x^{3}-16x^{2}-64x$$

Divide both sides by yx.

$$\frac{xyf}{xy}=\frac{x\left(x-4\right)\left(x+4\right)^{2}}{xy}$$

Dividing by yx undoes the multiplication by yx.

$$f=\frac{x\left(x-4\right)\left(x+4\right)^{2}}{xy}$$

Divide x\left(-4+x\right)\left(4+x\right)^{2} by yx.

$$f=\frac{\left(x-4\right)\left(x+4\right)^{2}}{y}$$