Solve (x+1)*(x+3)=x^2+13cm^2

$$( x + 1 ) \cdot ( x + 3 ) = x ^ { 2 } + 13 cm ^ { 2 }$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{4x+3}{13m^{2}}\text{, }&m\neq 0\\c\in \mathrm{C}\text{, }&x=-\frac{3}{4}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by x+3 and combine like terms.

$$x^{2}+4x+3=x^{2}+13cm^{2}$$

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

$$x^{2}+13cm^{2}=x^{2}+4x+3$$

Subtract x^{2} from both sides.

$$13cm^{2}=x^{2}+4x+3-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$13cm^{2}=4x+3$$

The equation is in standard form.

$$13m^{2}c=4x+3$$

Divide both sides by 13m^{2}.

$$\frac{13m^{2}c}{13m^{2}}=\frac{4x+3}{13m^{2}}$$

Dividing by 13m^{2} undoes the multiplication by 13m^{2}.

$$c=\frac{4x+3}{13m^{2}}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{4x+3}{13m^{2}}\text{, }&m\neq 0\\c\in \mathrm{R}\text{, }&x=-\frac{3}{4}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by x+3 and combine like terms.

$$x^{2}+4x+3=x^{2}+13cm^{2}$$

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

$$x^{2}+13cm^{2}=x^{2}+4x+3$$

Subtract x^{2} from both sides.

$$13cm^{2}=x^{2}+4x+3-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$13cm^{2}=4x+3$$

The equation is in standard form.

$$13m^{2}c=4x+3$$

Divide both sides by 13m^{2}.

$$\frac{13m^{2}c}{13m^{2}}=\frac{4x+3}{13m^{2}}$$

Dividing by 13m^{2} undoes the multiplication by 13m^{2}.

$$c=\frac{4x+3}{13m^{2}}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{ic^{-\frac{1}{2}}\sqrt{-52x-39}}{13}\text{; }m=\frac{ic^{-\frac{1}{2}}\sqrt{-52x-39}}{13}\text{, }&c\neq 0\\m\in \mathrm{C}\text{, }&x=-\frac{3}{4}\text{ and }c=0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\sqrt{\frac{13\left(4x+3\right)}{c}}}{13}\text{; }m=-\frac{\sqrt{\frac{13\left(4x+3\right)}{c}}}{13}\text{, }&\left(x\geq -\frac{3}{4}\text{ and }c>0\right)\text{ or }\left(x\leq -\frac{3}{4}\text{ and }c<0\right)\\m\in \mathrm{R}\text{, }&x=-\frac{3}{4}\text{ and }c=0\end{matrix}\right.$$