Solve E=3(lambdac+2Deltac)

$$E = 3 ( \lambda c + 2 \Delta c )$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{E}{3\left(2\Delta +\lambda \right)}\text{, }&\lambda \neq -2\Delta \\c\in \mathrm{C}\text{, }&E=0\text{ and }\lambda =-2\Delta \end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by \lambda c+2\Delta c.

$$E=3\lambda c+6\Delta c$$

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

$$3\lambda c+6\Delta c=E$$

Combine all terms containing c.

$$\left(3\lambda +6\Delta \right)c=E$$

The equation is in standard form.

$$\left(6\Delta +3\lambda \right)c=E$$

Divide both sides by 3\lambda +6\Delta .

$$\frac{\left(6\Delta +3\lambda \right)c}{6\Delta +3\lambda }=\frac{E}{6\Delta +3\lambda }$$

Dividing by 3\lambda +6\Delta undoes the multiplication by 3\lambda +6\Delta .

$$c=\frac{E}{6\Delta +3\lambda }$$

Divide E by 3\lambda +6\Delta .

$$c=\frac{E}{3\left(2\Delta +\lambda \right)}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{E}{3\left(2\Delta +\lambda \right)}\text{, }&\lambda \neq -2\Delta \\c\in \mathrm{R}\text{, }&E=0\text{ and }\lambda =-2\Delta \end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by \lambda c+2\Delta c.

$$E=3\lambda c+6\Delta c$$

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

$$3\lambda c+6\Delta c=E$$

Combine all terms containing c.

$$\left(3\lambda +6\Delta \right)c=E$$

The equation is in standard form.

$$\left(6\Delta +3\lambda \right)c=E$$

Divide both sides by 3\lambda +6\Delta .

$$\frac{\left(6\Delta +3\lambda \right)c}{6\Delta +3\lambda }=\frac{E}{6\Delta +3\lambda }$$

Dividing by 3\lambda +6\Delta undoes the multiplication by 3\lambda +6\Delta .

$$c=\frac{E}{6\Delta +3\lambda }$$

Divide E by 3\lambda +6\Delta .

$$c=\frac{E}{3\left(2\Delta +\lambda \right)}$$

Solve for E

$$E=3c\left(2\Delta +\lambda \right)$$