Solve h(k+6)=3h-kf^prime2

$$h ( k + 6 ) = 3 h - k f ^ { \prime } 2$$

Solve for h (complex solution)

$$\left\{\begin{matrix}\\h=0\text{, }&\text{unconditionally}\\h\in \mathrm{C}\text{, }&k=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply h by k+6.

$$hk+6h=3h-k\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2$$

Subtract 3h from both sides.

$$hk+6h-3h=-k\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2$$

Combine 6h and -3h to get 3h.

$$hk+3h=-k\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2$$

Multiply -1 and 2 to get -2.

$$hk+3h=-2k\frac{\mathrm{d}}{\mathrm{d}x}(f)$$

Combine all terms containing h.

$$\left(k+3\right)h=-2k\frac{\mathrm{d}}{\mathrm{d}x}(f)$$

The equation is in standard form.

$$\left(k+3\right)h=0$$

Divide 0 by k+3.

$$h=0$$

Solve for h

$$\left\{\begin{matrix}\\h=0\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&k=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply h by k+6.

$$hk+6h=3h-k\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2$$

Subtract 3h from both sides.

$$hk+6h-3h=-k\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2$$

Combine 6h and -3h to get 3h.

$$hk+3h=-k\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2$$

Multiply -1 and 2 to get -2.

$$hk+3h=-2k\frac{\mathrm{d}}{\mathrm{d}x}(f)$$

Combine all terms containing h.

$$\left(k+3\right)h=-2k\frac{\mathrm{d}}{\mathrm{d}x}(f)$$

The equation is in standard form.

$$\left(k+3\right)h=0$$

Divide 0 by k+3.

$$h=0$$

Solve for f (complex solution)

$$f\in \mathrm{C}$$

$$k=-3\text{ or }h=0$$

Solve for f

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

$$k=-3\text{ or }h=0$$