(x - 3) (x + 1) ( x - 4) (x + 2) = - 6
(x^2 - 2x - 3) (x^2 - 2x - 8) = - 6
Let x^2 - 2x = a
So we have
(a - 3) (a - 8) = - 6
a^2 - 11a + 24 = -6
a^2 - 11a + 30 = 0 factor
(a - 5) ( a - 6) = 0
Setting each factor to 0 and solving for x produces
a = 5 or a =6
So
x^2 - 2x = 5 or x^2 - 2x = 6
complete the square on x
x^2 - 2x + 1 = 5 + 1 x^2 - 2x + 1 = 6 + 1
(x - 1)^2 = 6 (x - 1)^2 = 7
take both roots
x - 1 = ±√6 x - 1 = ±√7
x = ±√6 + 1 or x = ±√7 + 1