solve (x+2)(x+3)(x+8)(x+12)=4x^2?

we see 2 * 12 = 3 * 8 = 24

so group as follow

(x+2)(x+12)(x+3)(x+8)=4x^2

=> (x^2 + 14 x + 24) (x^2 + 11x + 24) = 4x^2
let x^2 + 11x +24 be y
(y+ 3x) y = 4x^2
y^2 + 3xy - 4x^2 = 0
(y- x)(y+ 4x) = 0

y =x => x^2 + 11x + 24 = x => x^2 + 10x + 24 = 0 => (x+4)(x+6) = 0 => x = -4 or - 6

y+ 4x = 0 => x^2 + 15x + 24 = 0

this can be solved for complex solutions

x = -15/2 - SQRT(129)/2 or x = -15/2 + SQRT(129)/2