Solve for P (complex solution)
\left\{\begin{matrix}P=-\frac{5\left(3x^{2}-120x-10\right)}{g}\text{, }&g\neq 0\\P\in \mathrm{C}\text{, }&\left(x=-\frac{11\sqrt{30}}{3}+20\text{ or }x=\frac{11\sqrt{30}}{3}+20\right)\text{ and }g=0\end{matrix}\right.
Solve for g (complex solution)
\left\{\begin{matrix}g=-\frac{5\left(3x^{2}-120x-10\right)}{P}\text{, }&P\neq 0\\g\in \mathrm{C}\text{, }&\left(x=-\frac{11\sqrt{30}}{3}+20\text{ or }x=\frac{11\sqrt{30}}{3}+20\right)\text{ and }P=0\end{matrix}\right.
Solve for P
\left\{\begin{matrix}P=-\frac{5\left(3x^{2}-120x-10\right)}{g}\text{, }&g\neq 0\\P\in \mathrm{R}\text{, }&\left(x=-\frac{11\sqrt{30}}{3}+20\text{ or }x=\frac{11\sqrt{30}}{3}+20\right)\text{ and }g=0\end{matrix}\right.
Solve for g
\left\{\begin{matrix}g=-\frac{5\left(3x^{2}-120x-10\right)}{P}\text{, }&P\neq 0\\g\in \mathrm{R}\text{, }&\left(x=-\frac{11\sqrt{30}}{3}+20\text{ or }x=\frac{11\sqrt{30}}{3}+20\right)\text{ and }P=0\end{matrix}\right.
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gP=50+600x-15x^{2}
The equation is in standard form.
\frac{gP}{g}=\frac{50+600x-15x^{2}}{g}
Divide both sides by g.
P=\frac{50+600x-15x^{2}}{g}
Dividing by g undoes the multiplication by g.
P=\frac{5\left(10+120x-3x^{2}\right)}{g}
Divide -15x^{2}+600x+50 by g.
Pg=50+600x-15x^{2}
The equation is in standard form.
\frac{Pg}{P}=\frac{50+600x-15x^{2}}{P}
Divide both sides by P.
g=\frac{50+600x-15x^{2}}{P}
Dividing by P undoes the multiplication by P.
g=\frac{5\left(10+120x-3x^{2}\right)}{P}
Divide -15x^{2}+600x+50 by P.
gP=50+600x-15x^{2}
The equation is in standard form.
\frac{gP}{g}=\frac{50+600x-15x^{2}}{g}
Divide both sides by g.
P=\frac{50+600x-15x^{2}}{g}
Dividing by g undoes the multiplication by g.
P=\frac{5\left(10+120x-3x^{2}\right)}{g}
Divide -15x^{2}+600x+50 by g.
Pg=50+600x-15x^{2}
The equation is in standard form.
\frac{Pg}{P}=\frac{50+600x-15x^{2}}{P}
Divide both sides by P.
g=\frac{50+600x-15x^{2}}{P}
Dividing by P undoes the multiplication by P.
g=\frac{5\left(10+120x-3x^{2}\right)}{P}
Divide -15x^{2}+600x+50 by P.
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