Solve for U
\left\{\begin{matrix}U=-\frac{10iU_{4}}{3f}\text{, }&f\neq 0\\U\in \mathrm{C}\text{, }&U_{4}=0\text{ and }f=0\end{matrix}\right.
Solve for U_4
U_{4}=\frac{3iUf}{10}
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U_{4}=\frac{3}{10}fiU
Multiply 1 and \frac{3}{10} to get \frac{3}{10}.
U_{4}=\frac{3}{10}ifU
Multiply \frac{3}{10} and i to get \frac{3}{10}i.
\frac{3}{10}ifU=U_{4}
Swap sides so that all variable terms are on the left hand side.
\frac{3if}{10}U=U_{4}
The equation is in standard form.
\frac{10\times \frac{3if}{10}U}{3if}=\frac{10U_{4}}{3if}
Divide both sides by \frac{3}{10}if.
U=\frac{10U_{4}}{3if}
Dividing by \frac{3}{10}if undoes the multiplication by \frac{3}{10}if.
U=-\frac{10iU_{4}}{3f}
Divide U_{4} by \frac{3}{10}if.
U_{4}=\frac{3}{10}fiU
Multiply 1 and \frac{3}{10} to get \frac{3}{10}.
U_{4}=\frac{3}{10}ifU
Multiply \frac{3}{10} and i to get \frac{3}{10}i.
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