Solve -l_{1}*F_{q}+(h+l_{2})*F=0

$$- l _ { 1 } \cdot F _ { q } + ( h + l _ { 2 } ) \cdot F = 0$$

Solve for F

$$\left\{\begin{matrix}F=\frac{F_{q}l_{1}}{h+l_{2}}\text{, }&h\neq -l_{2}\\F\in \mathrm{R}\text{, }&\left(F_{q}=0\text{ or }l_{1}=0\right)\text{ and }h=-l_{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply h+l_{2} by F.

$$\left(-l_{1}\right)F_{q}+hF+l_{2}F=0$$

Subtract \left(-l_{1}\right)F_{q} from both sides. Anything subtracted from zero gives its negation.

$$hF+l_{2}F=-\left(-l_{1}\right)F_{q}$$

Multiply -1 and -1 to get 1.

$$hF+l_{2}F=l_{1}F_{q}$$

Combine all terms containing F.

$$\left(h+l_{2}\right)F=l_{1}F_{q}$$

The equation is in standard form.

$$\left(h+l_{2}\right)F=F_{q}l_{1}$$

Divide both sides by h+l_{2}.

$$\frac{\left(h+l_{2}\right)F}{h+l_{2}}=\frac{F_{q}l_{1}}{h+l_{2}}$$

Dividing by h+l_{2} undoes the multiplication by h+l_{2}.

$$F=\frac{F_{q}l_{1}}{h+l_{2}}$$

Solve for F_q

$$\left\{\begin{matrix}F_{q}=\frac{F\left(h+l_{2}\right)}{l_{1}}\text{, }&l_{1}\neq 0\\F_{q}\in \mathrm{R}\text{, }&\left(h=-l_{2}\text{ or }F=0\right)\text{ and }l_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply h+l_{2} by F.

$$\left(-l_{1}\right)F_{q}+hF+l_{2}F=0$$

Subtract hF from both sides. Anything subtracted from zero gives its negation.

$$\left(-l_{1}\right)F_{q}+l_{2}F=-hF$$

Subtract l_{2}F from both sides.

$$\left(-l_{1}\right)F_{q}=-hF-l_{2}F$$

Reorder the terms.

$$-F_{q}l_{1}=-Fh-Fl_{2}$$

The equation is in standard form.

$$\left(-l_{1}\right)F_{q}=-Fh-Fl_{2}$$

Divide both sides by -l_{1}.

$$\frac{\left(-l_{1}\right)F_{q}}{-l_{1}}=-\frac{F\left(h+l_{2}\right)}{-l_{1}}$$

Dividing by -l_{1} undoes the multiplication by -l_{1}.

$$F_{q}=-\frac{F\left(h+l_{2}\right)}{-l_{1}}$$

Divide -F\left(h+l_{2}\right) by -l_{1}.

$$F_{q}=\frac{F\left(h+l_{2}\right)}{l_{1}}$$