Solve b/c=2b

$$\frac { b } { c } = 2 b$$

Solve for b

$$\left\{\begin{matrix}b=0\text{, }&c\neq 0\\b\in \mathrm{R}\text{, }&c=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by c.

$$b=2bc$$

Subtract 2bc from both sides.

$$b-2bc=0$$

Combine all terms containing b.

$$\left(1-2c\right)b=0$$

Divide 0 by 1-2c.

$$b=0$$

Solve for c

$$\left\{\begin{matrix}\\c=\frac{1}{2}\text{, }&\text{unconditionally}\\c\neq 0\text{, }&b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by c.

$$b=2bc$$

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

$$2bc=b$$

Divide both sides by 2b.

$$\frac{2bc}{2b}=\frac{b}{2b}$$

Dividing by 2b undoes the multiplication by 2b.

$$c=\frac{b}{2b}$$

Divide b by 2b.

$$c=\frac{1}{2}$$