Solve e^x=-2e^x-2c

$$e ^ { x } = - 2 e ^ { x } - 2 c$$

Solve for c

$$c=-\frac{3e^{x}}{2}$$

Steps for Solving Linear Equation

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

$$-2e^{x}-2c=e^{x}$$

Add 2e^{x} to both sides.

$$-2c=e^{x}+2e^{x}$$

Combine e^{x} and 2e^{x} to get 3e^{x}.

$$-2c=3e^{x}$$

Divide both sides by -2.

$$\frac{-2c}{-2}=\frac{3e^{x}}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$c=\frac{3e^{x}}{-2}$$

Divide 3e^{x} by -2.

$$c=-\frac{3e^{x}}{2}$$

Solve for x (complex solution)

$$x=\ln(-\frac{2c}{3})+2\pi n_{1}i$$

$$n_{1}\in \mathrm{Z}$$

$$c\neq 0$$

Solve for x

$$x=\ln(-\frac{2c}{3})$$

$$c<0$$