Solve (V_{c}*7l)-(P*4l)-(P*2l)=0

$$( V _ { c } \times 7 l ) - ( P \times 4 l ) - ( P \times 2 l ) = 0$$

Solve for P

$$\left\{\begin{matrix}\\P=\frac{7V_{c}}{6}\text{, }&\text{unconditionally}\\P\in \mathrm{R}\text{, }&l=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply -1 and 4 to get -4.

$$V_{c}\times 7l-4Pl-P\times 2l=0$$

Multiply -1 and 2 to get -2.

$$V_{c}\times 7l-4Pl-2Pl=0$$

Combine -4Pl and -2Pl to get -6Pl.

$$V_{c}\times 7l-6Pl=0$$

Subtract V_{c}\times 7l from both sides. Anything subtracted from zero gives its negation.

$$-6Pl=-V_{c}\times 7l$$

The equation is in standard form.

$$\left(-6l\right)P=-7V_{c}l$$

Divide both sides by -6l.

$$\frac{\left(-6l\right)P}{-6l}=-\frac{7V_{c}l}{-6l}$$

Dividing by -6l undoes the multiplication by -6l.

$$P=-\frac{7V_{c}l}{-6l}$$

Divide -7V_{c}l by -6l.

$$P=\frac{7V_{c}}{6}$$

Solve for V_c

$$\left\{\begin{matrix}\\V_{c}=\frac{6P}{7}\text{, }&\text{unconditionally}\\V_{c}\in \mathrm{R}\text{, }&l=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add P\times 2l to both sides.

$$V_{c}\times 7l-P\times 4l=0+P\times 2l$$

Anything plus zero gives itself.

$$V_{c}\times 7l-P\times 4l=P\times 2l$$

Add P\times 4l to both sides.

$$V_{c}\times 7l=P\times 2l+P\times 4l$$

Combine P\times 2l and P\times 4l to get 6Pl.

$$V_{c}\times 7l=6Pl$$

The equation is in standard form.

$$7lV_{c}=6Pl$$

Divide both sides by 7l.

$$\frac{7lV_{c}}{7l}=\frac{6Pl}{7l}$$

Dividing by 7l undoes the multiplication by 7l.

$$V_{c}=\frac{6Pl}{7l}$$

Divide 6Pl by 7l.

$$V_{c}=\frac{6P}{7}$$