(x+1) (x+3) (x+4) (x+6) = 72

Find the real root of (x+1) (x+3) (x+4) (x+6) = 72 if any.

(x+1) (x+6) (x+3) (x+4) = 72

(x²+7x+6) (x²+7x+12) = 72

let, x²+7x+6 = g

g (g+6) = 72

g²+6g-72 = 0

(g-6) (g+12) = 0

g = 6, -12

recall, x²+7x+6 = g

x²+7x+6 = 6

x²+7x = 0

x (x+7) = 0

x = 0, -7

g = -12 will give 2 imaginary roots.