Question

$( {x}^{2} + x)( {x}^{2} + x - 2) = 24$
Find roots

Answer 1

(x^2+x)(x^2+x-2) = 24

let we suppose

if (x^2 + x ) = A

then

(A)(A-2) = 24
A^2-2A-24 = 0
A^2 - 6A + 4A - 24 = 0
(A-6)(A+4) = 0
A = 6,-4

(x^2 + x ) = 6 ---------> EQ.(1)
(x^2 + x ) = -4 ---------> EQ.(2)

from EQ.(1)

x^2+x-6 = 0
(x+3)(x-2)= 0

x = -3,2

from EQ.(2)

x^2+x+4 = 0

x = (-1+- √1-16) / 2
= (-1+- i√15) / 2

x = (-1+i√15) / 2 , (-1-i√15) / 2