The given equation is:

$\sin^2(2x) - 5\sin(2x)\cos(2x) + 6\cos^2(2x) = 0$

Solution Steps:

1. Rewrite using a trigonometric identity: Use $\sin^2(2x) + \cos^2(2x) = 1$ to replace $\sin^2(2x)$ in the equation: $(1 - \cos^2(2x)) - 5\sin(2x)\cos(2x) + 6\cos^2(2x) = 0$

2. Simplify: Expand and combine like terms: $1 - \cos^2(2x) - 5\sin(2x)\cos(2x) + 6\cos^2(2x) = 0$ $1 + 5\cos^2(2x) - 5\sin(2x)\cos(2x) = 0$

3. Factorize: Let $\cos(2x) = u$ and $\sin(2x) = \sqrt{1-u^2}$. Substitute and solve the quadratic.

Would you like to proceed step by step into the detailed calculations? Or would you prefer I jump to the solutions for $x$?