Solve -f(x)=6x^3+2x^2-14x

$$- f ( x ) = 6 x ^ { 3 } + 2 x ^ { 2 } - 14 x$$

Solve for f (complex solution)

$$\left\{\begin{matrix}\\f=14-2x-6x^{2}\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$-fx=6x^{3}+2x^{2}-14x$$

The equation is in standard form.

$$\left(-x\right)f=6x^{3}+2x^{2}-14x$$

Divide both sides by -x.

$$\frac{\left(-x\right)f}{-x}=\frac{2x\left(3x^{2}+x-7\right)}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$f=\frac{2x\left(3x^{2}+x-7\right)}{-x}$$

Divide 2x\left(3x^{2}+x-7\right) by -x.

$$f=14-2x-6x^{2}$$

Solve for f

$$\left\{\begin{matrix}\\f=14-2x-6x^{2}\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$-fx=6x^{3}+2x^{2}-14x$$

The equation is in standard form.

$$\left(-x\right)f=6x^{3}+2x^{2}-14x$$

Divide both sides by -x.

$$\frac{\left(-x\right)f}{-x}=\frac{2x\left(3x^{2}+x-7\right)}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$f=\frac{2x\left(3x^{2}+x-7\right)}{-x}$$

Divide 2x\left(3x^{2}+x-7\right) by -x.

$$f=14-2x-6x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{85-6f}-1}{6}$$

$$x=0$$

$$x=\frac{-\sqrt{85-6f}-1}{6}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{-\sqrt{85-6f}-1}{6}\text{; }x=\frac{\sqrt{85-6f}-1}{6}\text{, }&f\leq \frac{85}{6}\end{matrix}\right.$$