TITLE: How to solve a quartic equation?
QUESTION [13 upvotes]: Could someone please explain how to solve this : $x^4 - 10x^3 + 21x^2 + 40x - 100 = 0$ - not the answer only, but a step-by-step solution.
 I tried to solve it, with the help of khanacademy, but still I have no idea how to correctly solve it.
Thank you so much in advance!

REPLY [8 votes]: $$x^4-10x^3 +25x^2-(4x^2-40x+100)=0$$
$$\Rightarrow x^2(x^2-10x+25)-4(x^2-10x+25)=0 $$
$$\Rightarrow (x^2-4)(x^2-10x+25)=0 $$
$$\Rightarrow (x-2)(x+2)(x-5)^2=0 $$
$$\Rightarrow x_1=-2 , x_2=2 , x_{3,4}=5$$