Solve -f(x)=(-2x^3+3x)(5x^3-2x)

$$- f ( x ) = ( - 2 x ^ { 3 } + 3 x ) ( 5 x ^ { 3 } - 2 x )$$

Solve for f

$$\left\{\begin{matrix}\\f=x\left(10x^{4}-19x^{2}+6\right)\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2x^{3}+3x by 5x^{3}-2x and combine like terms.

$$\left(-f\right)x=-10x^{6}+19x^{4}-6x^{2}$$

Reorder the terms.

$$-fx=-10x^{6}+19x^{4}-6x^{2}$$

The equation is in standard form.

$$\left(-x\right)f=-10x^{6}+19x^{4}-6x^{2}$$

Divide both sides by -x.

$$\frac{\left(-x\right)f}{-x}=\frac{x^{2}\left(-10x^{4}+19x^{2}-6\right)}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$f=\frac{x^{2}\left(-10x^{4}+19x^{2}-6\right)}{-x}$$

Divide x^{2}\left(-10x^{4}+19x^{2}-6\right) by -x.

$$f=10x^{5}-19x^{3}+6x$$