9^{3x+2} \cdot 5^{10x+4}=15^{3x+2} \cdot 25 ^{2x}\\\\3^{2(3x+2)} \cdot 5^{10x+4}=3^{3x+2} \cdot 5^{3x+2} \cdot 5^{2\cdot 2x} \\\\ 3^{6x+4} \cdot 5^{10x+4}=3^{3x+2} \cdot 5^{3x+2} \cdot 5^{4x}
3^{6x+4} \cdot 5^{10x+4}=3^{3x+2} \cdot 5^{7x+2} | (): 3^{3x+2} \cdot 5^{7x+2} obie strony równania
\frac{3^{6x+4} \cdot 5^{10x+4}}{3^{3x+2} \cdot 5^{7x+2} }=\frac{3^{3x+4} \cdot 5^{7x+2}}{3^{3x+2} \cdot 5^{7x+2} } \\\\ 3^{6x+2-(3x+2)} \cdot 5^{10x+4-(7x+2)}=1\\\\ 3^{6x+4-3x-2} \cdot 5^{10x+4-7x-2}=1 \\\\ 3^{3x+2} \cdot 5^{3x+2}=1 \\\\ (3 \cdot 5)^{3x+2}=1 \\\\15^{3x+2}=15^0 \\\\ 3x+2=0 \\\\ 3x=-2 \\\\ x=-\frac{2}{3}