Перепишем так:
(x+2)(x+12)*(x+3)(x+8) = 4x^2
(x^2+14x+24)(x^2+11x+24) = 4x^2
Замена x^2 + 14x + 24 = t
t(t-3x) - 4x^2 = 0
t^2 - 3tx - 4x^2 = 0
Делим все на x^2
(t/x)^2 - 3(t/x) - 4 = 0
Квадратное уравнение относительно (t/x)
(t/x + 1)(t/x - 4) = 0
1) t/x = (x^2 + 14x + 24)/x = -1
x^2 + 14x + 24 = -x
x^2 + 15x + 24 = 0
D = 15^2 - 4*24 = 225 - 96 = 129
x1 = (-15 - √129)/2
x2 = (-15 + √129)/2
2) t/x = (x^2 + 14x + 24)/x = 4
x^2 + 14x + 24 = 4x
x^2 + 10x + 24 = 0
(x + 4)(x + 6) = 0
x3 = -4; x4 = -6