Solve for a
\left\{\begin{matrix}a=\frac{iwl^{2}}{gy}\text{, }&y\neq 0\text{ and }g\neq 0\\a\in \mathrm{C}\text{, }&\left(w=0\text{ and }y=0\right)\text{ or }\left(l=0\text{ and }y=0\right)\text{ or }\left(l=0\text{ and }g=0\text{ and }y\neq 0\right)\text{ or }\left(w=0\text{ and }g=0\text{ and }y\neq 0\right)\end{matrix}\right.
Solve for g
\left\{\begin{matrix}g=\frac{iwl^{2}}{ay}\text{, }&y\neq 0\text{ and }a\neq 0\\g\in \mathrm{C}\text{, }&\left(w=0\text{ and }y=0\right)\text{ or }\left(l=0\text{ and }y=0\right)\text{ or }\left(l=0\text{ and }a=0\text{ and }y\neq 0\right)\text{ or }\left(w=0\text{ and }a=0\text{ and }y\neq 0\right)\end{matrix}\right.
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wil^{2}=gay
Multiply l and l to get l^{2}.
gay=wil^{2}
Swap sides so that all variable terms are on the left hand side.
gya=iwl^{2}
The equation is in standard form.
\frac{gya}{gy}=\frac{iwl^{2}}{gy}
Divide both sides by gy.
a=\frac{iwl^{2}}{gy}
Dividing by gy undoes the multiplication by gy.
wil^{2}=gay
Multiply l and l to get l^{2}.
gay=wil^{2}
Swap sides so that all variable terms are on the left hand side.
ayg=iwl^{2}
The equation is in standard form.
\frac{ayg}{ay}=\frac{iwl^{2}}{ay}
Divide both sides by ay.
g=\frac{iwl^{2}}{ay}
Dividing by ay undoes the multiplication by ay.
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