Solve B=qc(1-d/l)

$$B = q c ( 1 - \frac { d } { l } )$$

Solve for c

$$\left\{\begin{matrix}c=-\frac{Bl}{q\left(d-l\right)}\text{, }&d\neq l\text{ and }q\neq 0\text{ and }l\neq 0\\c\in \mathrm{R}\text{, }&\left(d=l\text{ or }q=0\right)\text{ and }B=0\text{ and }l\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by l.

$$Bl=qc\left(1-\frac{d}{l}\right)l$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{l}{l}.

$$Bl=qc\left(\frac{l}{l}-\frac{d}{l}\right)l$$

Since \frac{l}{l} and \frac{d}{l} have the same denominator, subtract them by subtracting their numerators.

$$Bl=qc\times \frac{l-d}{l}l$$

Express q\times \frac{l-d}{l} as a single fraction.

$$Bl=\frac{q\left(l-d\right)}{l}cl$$

Express \frac{q\left(l-d\right)}{l}l as a single fraction.

$$Bl=\frac{q\left(l-d\right)l}{l}c$$

Cancel out l in both numerator and denominator.

$$Bl=q\left(l-d\right)c$$

Use the distributive property to multiply q by l-d.

$$Bl=\left(ql-qd\right)c$$

Use the distributive property to multiply ql-qd by c.

$$Bl=qlc-qdc$$

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

$$qlc-qdc=Bl$$

Combine all terms containing c.

$$\left(ql-qd\right)c=Bl$$

The equation is in standard form.

$$\left(lq-dq\right)c=Bl$$

Divide both sides by ql-qd.

$$\frac{\left(lq-dq\right)c}{lq-dq}=\frac{Bl}{lq-dq}$$

Dividing by ql-qd undoes the multiplication by ql-qd.

$$c=\frac{Bl}{lq-dq}$$

Divide Bl by ql-qd.

$$c=\frac{Bl}{q\left(l-d\right)}$$

Solve for B

$$B=\frac{cq\left(l-d\right)}{l}$$

$$l\neq 0$$