Question

solve (x^3)+(12x^2)+(21x)-(4)=(x^4)-(2x^3)-(13x^2)-(4)
the answers are x=-1,-3,7,0 but i need to know how to do it

Answer 1

x^4 -3x^3 -25 x^2 -21 x = 0
x ( x^3 -3 x^2 -25 x -21) = 0
so we know x = 0 is a solution
Guess -1 solution
(You can see that x^3 -3 x^2 -25 x -21 is 0 for x = -1)

then we know (x+1) is a factor of
x^3 -3 x^2 -25 x -21
so do long division
(x^3 -3 x^2 -25 x -21)/(x+1) =
x^2-4x-21
(x+3)(x-7) = 0
so
x = -3 or +7

Answer 2

By the way, you could guess the seven and three immediately from the 21 but I saw the -1 first.