Solve 600-2kx+32k-9600/x=216

$$600-2kx+32k- \frac{ 9600 }{ x } = 216$$

Solve for k

$$k=-\frac{192\left(x-25\right)}{x\left(16-x\right)}$$

$$x\neq 16\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$x\times 600-2kxx+32kx-9600=216x$$

Multiply x and x to get x^{2}.

$$x\times 600-2kx^{2}+32kx-9600=216x$$

Subtract x\times 600 from both sides.

$$-2kx^{2}+32kx-9600=216x-x\times 600$$

Combine 216x and -x\times 600 to get -384x.

$$-2kx^{2}+32kx-9600=-384x$$

Add 9600 to both sides.

$$-2kx^{2}+32kx=-384x+9600$$

Combine all terms containing k.

$$\left(-2x^{2}+32x\right)k=-384x+9600$$

The equation is in standard form.

$$\left(32x-2x^{2}\right)k=9600-384x$$

Divide both sides by -2x^{2}+32x.

$$\frac{\left(32x-2x^{2}\right)k}{32x-2x^{2}}=\frac{9600-384x}{32x-2x^{2}}$$

Dividing by -2x^{2}+32x undoes the multiplication by -2x^{2}+32x.

$$k=\frac{9600-384x}{32x-2x^{2}}$$

Divide -384x+9600 by -2x^{2}+32x.

$$k=\frac{192\left(25-x\right)}{x\left(16-x\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{8\left(\sqrt{\left(k-48\right)\left(k-3\right)}-k-12\right)}{k}\text{; }x=\frac{8\left(\sqrt{\left(k-48\right)\left(k-3\right)}+k+12\right)}{k}\text{, }&k\neq 0\\x=25\text{, }&k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{8\left(\sqrt{\left(k-48\right)\left(k-3\right)}-k-12\right)}{k}\text{; }x=\frac{8\left(\sqrt{\left(k-48\right)\left(k-3\right)}+k+12\right)}{k}\text{, }&k\geq 48\text{ or }\left(k\neq 0\text{ and }k\leq 3\right)\\x=25\text{, }&k=0\end{matrix}\right.$$