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-gx=x^{2}-5-4x
Subtract 4x from both sides.
\left(-x\right)g=x^{2}-4x-5
The equation is in standard form.
\frac{\left(-x\right)g}{-x}=\frac{\left(x-5\right)\left(x+1\right)}{-x}
Divide both sides by -x.
g=\frac{\left(x-5\right)\left(x+1\right)}{-x}
Dividing by -x undoes the multiplication by -x.
g=-\frac{\left(x-5\right)\left(x+1\right)}{x}
Divide \left(-5+x\right)\left(1+x\right) by -x.