Solve for f (complex solution)
\left\{\begin{matrix}f=-\frac{x^{2}+10x-5c}{hx}\text{, }&x\neq 0\text{ and }h\neq 0\\f\in \mathrm{C}\text{, }&\left(c=0\text{ and }x=0\right)\text{ or }\left(c=\frac{x\left(x+10\right)}{5}\text{ and }h=0\text{ and }x\neq 0\right)\end{matrix}\right.
Solve for c
c=\frac{x\left(x+fh+10\right)}{5}
Solve for f
\left\{\begin{matrix}f=-\frac{x^{2}+10x-5c}{hx}\text{, }&x\neq 0\text{ and }h\neq 0\\f\in \mathrm{R}\text{, }&\left(c=0\text{ and }x=0\right)\text{ or }\left(c=\frac{x\left(x+10\right)}{5}\text{ and }h=0\text{ and }x\neq 0\right)\end{matrix}\right.
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hxf=5c-10x-x^{2}
The equation is in standard form.
\frac{hxf}{hx}=\frac{5c-10x-x^{2}}{hx}
Divide both sides by hx.
f=\frac{5c-10x-x^{2}}{hx}
Dividing by hx undoes the multiplication by hx.
-x^{2}-10x+5c=fhx
Swap sides so that all variable terms are on the left hand side.
-10x+5c=fhx+x^{2}
Add x^{2} to both sides.
5c=fhx+x^{2}+10x
Add 10x to both sides.
5c=x^{2}+fhx+10x
The equation is in standard form.
\frac{5c}{5}=\frac{x\left(x+fh+10\right)}{5}
Divide both sides by 5.
c=\frac{x\left(x+fh+10\right)}{5}
Dividing by 5 undoes the multiplication by 5.
hxf=5c-10x-x^{2}
The equation is in standard form.
\frac{hxf}{hx}=\frac{5c-10x-x^{2}}{hx}
Divide both sides by hx.
f=\frac{5c-10x-x^{2}}{hx}
Dividing by hx undoes the multiplication by hx.
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