Solve f^prime(x)=3x^2-2ax+3

$$f ^ { \prime } ( x ) = 3 x ^ { 2 } - 2 a x + 3$$

Solve for a

$$a=\frac{3x}{2}+\frac{3}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$3x^{2}-2ax+3=\frac{\mathrm{d}}{\mathrm{d}x}(f)x$$

Subtract 3x^{2} from both sides.

$$-2ax+3=\frac{\mathrm{d}}{\mathrm{d}x}(f)x-3x^{2}$$

Subtract 3 from both sides.

$$-2ax=\frac{\mathrm{d}}{\mathrm{d}x}(f)x-3x^{2}-3$$

The equation is in standard form.

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

Divide both sides by -2x.

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

Dividing by -2x undoes the multiplication by -2x.

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

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

$$a=\frac{3x}{2}+\frac{3}{2x}$$

Solve for f

$$f\in \mathrm{R}$$

$$a=\frac{3x}{2}+\frac{3}{2x}\text{ and }x\neq 0$$