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A user named ‘Uzdawi’ from another post asked a question about how to solve the quartic function of

$x^4 - 10x^3 + 21x^2 + 40x - 100 = 0$

One of the responses included an answer from the user ‘Peđa Terzić’, which is as follows:

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

Could anyone kindly elaborate on the method used to get to the answer please.

And how the same method could be used to solve the following function:

$x^4 + 10x^3 + 30x^2 + 25x + 100 = 0$

If not the same method used by Peđa Terzić, how else could you approach to solving a quartic function?

Thank you for your time.