AMO 2027 Grades 9-11 SET 5 - Self-study Question 15

For positive real numbers $x,y,z$, $$\frac{x}{3y+2z}+\frac{3y}{x+2z}+\frac{2z}{x+3y}=\frac32.$$ Find $$\frac{(7x+12y)^2}{z^2}.$$

Enter one positive integer, without units.