Solve 168cm^2-60cm^2=23cmx+x^2

$$168 cm ^ { 2 } - 60 cm ^ { 2 } = 23 cm x + x ^ { 2 }$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{x^{2}}{m\left(108m-23x\right)}\text{, }&m\neq \frac{23x}{108}\text{ and }m\neq 0\\c\in \mathrm{C}\text{, }&x=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 168cm^{2} and -60cm^{2} to get 108cm^{2}.

$$108cm^{2}=23cmx+x^{2}$$

Subtract 23cmx from both sides.

$$108cm^{2}-23cmx=x^{2}$$

Combine all terms containing c.

$$\left(108m^{2}-23mx\right)c=x^{2}$$

Divide both sides by -23xm+108m^{2}.

$$\frac{\left(108m^{2}-23mx\right)c}{108m^{2}-23mx}=\frac{x^{2}}{108m^{2}-23mx}$$

Dividing by -23xm+108m^{2} undoes the multiplication by -23xm+108m^{2}.

$$c=\frac{x^{2}}{108m^{2}-23mx}$$

Divide x^{2} by -23xm+108m^{2}.

$$c=\frac{x^{2}}{m\left(108m-23x\right)}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{x^{2}}{m\left(108m-23x\right)}\text{, }&m\neq \frac{23x}{108}\text{ and }m\neq 0\\c\in \mathrm{R}\text{, }&x=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 168cm^{2} and -60cm^{2} to get 108cm^{2}.

$$108cm^{2}=23cmx+x^{2}$$

Subtract 23cmx from both sides.

$$108cm^{2}-23cmx=x^{2}$$

Combine all terms containing c.

$$\left(108m^{2}-23mx\right)c=x^{2}$$

Divide both sides by -23xm+108m^{2}.

$$\frac{\left(108m^{2}-23mx\right)c}{108m^{2}-23mx}=\frac{x^{2}}{108m^{2}-23mx}$$

Dividing by -23xm+108m^{2} undoes the multiplication by -23xm+108m^{2}.

$$c=\frac{x^{2}}{108m^{2}-23mx}$$

Divide x^{2} by -23xm+108m^{2}.

$$c=\frac{x^{2}}{m\left(108m-23x\right)}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{\sqrt{c\left(529c+432\right)x^{2}}+23cx}{216c}\text{; }m=\frac{-\sqrt{c\left(529c+432\right)x^{2}}+23cx}{216c}\text{, }&c\neq 0\\m\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=\frac{x\left(\sqrt{c\left(529c+432\right)}+23c\right)}{216c}\text{; }m=\frac{x\left(-\sqrt{c\left(529c+432\right)}+23c\right)}{216c}\text{, }&c>0\text{ or }c\leq -\frac{432}{529}\\m=0\text{, }&x=0\\m\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$