Solve x^2+5x+6=56cm^2

$$x ^ { 2 } + 5 x + 6 = 56 cm ^ { 2 }$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{\left(x+2\right)\left(x+3\right)}{56m^{2}}\text{, }&m\neq 0\\c\in \mathrm{C}\text{, }&\left(x=-2\text{ or }x=-3\right)\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$56cm^{2}=x^{2}+5x+6$$

The equation is in standard form.

$$56m^{2}c=x^{2}+5x+6$$

Divide both sides by 56m^{2}.

$$\frac{56m^{2}c}{56m^{2}}=\frac{\left(x+2\right)\left(x+3\right)}{56m^{2}}$$

Dividing by 56m^{2} undoes the multiplication by 56m^{2}.

$$c=\frac{\left(x+2\right)\left(x+3\right)}{56m^{2}}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{\left(x+2\right)\left(x+3\right)}{56m^{2}}\text{, }&m\neq 0\\c\in \mathrm{R}\text{, }&\left(x=-2\text{ or }x=-3\right)\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$56cm^{2}=x^{2}+5x+6$$

The equation is in standard form.

$$56m^{2}c=x^{2}+5x+6$$

Divide both sides by 56m^{2}.

$$\frac{56m^{2}c}{56m^{2}}=\frac{\left(x+2\right)\left(x+3\right)}{56m^{2}}$$

Dividing by 56m^{2} undoes the multiplication by 56m^{2}.

$$c=\frac{\left(x+2\right)\left(x+3\right)}{56m^{2}}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{ic^{-\frac{1}{2}}\sqrt{-x-2}\sqrt{14\left(x+3\right)}}{28}\text{; }m=\frac{ic^{-\frac{1}{2}}\sqrt{-x-2}\sqrt{14\left(x+3\right)}}{28}\text{, }&c\neq 0\\m\in \mathrm{C}\text{, }&\left(x=-2\text{ or }x=-3\right)\text{ and }c=0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\sqrt{\frac{14\left(x+2\right)\left(x+3\right)}{c}}}{28}\text{; }m=-\frac{\sqrt{\frac{14\left(x+2\right)\left(x+3\right)}{c}}}{28}\text{, }&\left(x\geq -2\text{ and }c>0\right)\text{ or }\left(c>0\text{ and }x\leq -3\right)\text{ or }\left(x\leq -2\text{ and }x\geq -3\text{ and }c<0\right)\\m\in \mathrm{R}\text{, }&\left(x=-2\text{ or }x=-3\right)\text{ and }c=0\end{matrix}\right.$$