solve the equation in the complex number system
x^4+x^3+4x^2+10x-60=0
try x = 2
16+8+16 +20 - 60 = 0 sure enough x = 2 works
so divide by (x-2)
x^3 + 3 x^2 + 10 x + 30
write as
x^3+10 x +3(x^2 +10)
x(x^2+10) + 3(x^2+10)
(x+3)(x^2+10)
so
x = -3 is a root
left with x^2 = -10
x = +/- i sqrt(10)
so
2, -3, i sqrt 10 , -i sqrt 10