Solve for F
\left\{\begin{matrix}F=\frac{24\left(2H+7\right)}{s}\text{, }&s\neq 0\\F\in \mathrm{R}\text{, }&H=-\frac{7}{2}\text{ and }s=0\end{matrix}\right.
Solve for H
H=\frac{Fs-168}{48}
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Fs=28\times 6+8\times 6H
Do the multiplications.
Fs=168+8\times 6H
Multiply 28 and 6 to get 168.
Fs=168+48H
Multiply 8 and 6 to get 48.
sF=48H+168
The equation is in standard form.
\frac{sF}{s}=\frac{48H+168}{s}
Divide both sides by s.
F=\frac{48H+168}{s}
Dividing by s undoes the multiplication by s.
F=\frac{24\left(2H+7\right)}{s}
Divide 168+48H by s.
Fs=28\times 6+8\times 6H
Do the multiplications.
Fs=168+8\times 6H
Multiply 28 and 6 to get 168.
Fs=168+48H
Multiply 8 and 6 to get 48.
168+48H=Fs
Swap sides so that all variable terms are on the left hand side.
48H=Fs-168
Subtract 168 from both sides.
\frac{48H}{48}=\frac{Fs-168}{48}
Divide both sides by 48.
H=\frac{Fs-168}{48}
Dividing by 48 undoes the multiplication by 48.
H=\frac{Fs}{48}-\frac{7}{2}
Divide Fs-168 by 48.
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