Solve f_{1}x_{1}=-x^3/3+4x^2

$$f _ { 1 } x _ { 1 } = - \frac { x ^ { 3 } } { 3 } + 4 x ^ { 2 }$$

Solve for f_1

$$\left\{\begin{matrix}f_{1}=-\frac{\left(x-12\right)x^{2}}{3x_{1}}\text{, }&x_{1}\neq 0\\f_{1}\in \mathrm{R}\text{, }&\left(x=0\text{ or }x=12\right)\text{ and }x_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3f_{1}x_{1}=-x^{3}+12x^{2}$$

The equation is in standard form.

$$3x_{1}f_{1}=12x^{2}-x^{3}$$

Divide both sides by 3x_{1}.

$$\frac{3x_{1}f_{1}}{3x_{1}}=\frac{\left(12-x\right)x^{2}}{3x_{1}}$$

Dividing by 3x_{1} undoes the multiplication by 3x_{1}.

$$f_{1}=\frac{\left(12-x\right)x^{2}}{3x_{1}}$$