\(27^{x + 2} \div 9^{x + 1} = 3^{2x}\)

\(3^{3(x + 2)} \div 3^{2(x + 1)} = 3^{2x}\)

\(3^{3x + 6} \div 3^{2x + 2} = 3^{2x}\)

\(\therefore (3x + 6) - (2x + 2) = 2x\)

\(x + 4 = 2x \implies x = 4\)