Solve fa(x)=2*ax^3-(2-4a)x

$$f a ( x ) = 2 \cdot a x ^ { 3 } - ( 2 - 4 a ) x$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{2}{-2x^{2}+f-4}\text{, }&f\neq 2x^{2}+4\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2-4a by x.

$$fax=2ax^{3}-\left(2x-4ax\right)$$

To find the opposite of 2x-4ax, find the opposite of each term.

$$fax=2ax^{3}-2x+4ax$$

Subtract 2ax^{3} from both sides.

$$fax-2ax^{3}=-2x+4ax$$

Subtract 4ax from both sides.

$$fax-2ax^{3}-4ax=-2x$$

Combine all terms containing a.

$$\left(fx-2x^{3}-4x\right)a=-2x$$

The equation is in standard form.

$$\left(-2x^{3}+fx-4x\right)a=-2x$$

Divide both sides by fx-2x^{3}-4x.

$$\frac{\left(-2x^{3}+fx-4x\right)a}{-2x^{3}+fx-4x}=-\frac{2x}{-2x^{3}+fx-4x}$$

Dividing by fx-2x^{3}-4x undoes the multiplication by fx-2x^{3}-4x.

$$a=-\frac{2x}{-2x^{3}+fx-4x}$$

Divide -2x by fx-2x^{3}-4x.

$$a=-\frac{2}{-2x^{2}+f-4}$$

Solve for f

$$\left\{\begin{matrix}f=2x^{2}+4-\frac{2}{a}\text{, }&a\neq 0\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2-4a by x.

$$fax=2ax^{3}-\left(2x-4ax\right)$$

To find the opposite of 2x-4ax, find the opposite of each term.

$$fax=2ax^{3}-2x+4ax$$

The equation is in standard form.

$$axf=2ax^{3}+4ax-2x$$

Divide both sides by ax.

$$\frac{axf}{ax}=\frac{2x\left(ax^{2}+2a-1\right)}{ax}$$

Dividing by ax undoes the multiplication by ax.

$$f=\frac{2x\left(ax^{2}+2a-1\right)}{ax}$$

Divide 2x\left(ax^{2}-1+2a\right) by ax.

$$f=2x^{2}+4-\frac{2}{a}$$