# Math Help - reducing quadratic

-180x^2 + 12000x - 100000

What is the best way of reducing this down as much as possible so I more easily solve it ?

I see I could factor out 20 eg. 20(-90x^2 + 600x - 5000), but is there a more effective way of reducing it ?

thanks for any help.

Why not take out another factor of 10?

$-180x^2+12000x-100000$

Take out a factor of -180

$= -180\left (x^2-\frac{12000}{180}x+\frac{100000}{180} \right)$

$= -180\left (x^2-\frac{200}{3}x+\frac{5000}{9} \right)$

$= -180\left (x^2-\frac{200}{3}x+\frac{5000}{9} +\frac{40000}{36}-\frac{40000}{36}\right)$

$= -180\left( \frac{36x^2-24000x+40000}{36}-\frac{20000}{36}\right)$

$= -180\left[ \left(\frac{6x-200}{6}\right)^2-\left(\frac{100\sqrt{2}}{6}\right)^2 \right]$

Now, use difference of squares to factorize the expression.