[tex]2^{3x+7} + 5^{3x+4} + 2^{3x+5} - 5^{3x+5} = 0, \\ 2^{3x}\cdot2^{7} + 5^{3x}\cdot5^{4} + 2^{3x}\cdot2^{5} - 5^{3x}\cdot5^{5} = 0, \\ 128\cdot2^{3x} + 625\cdot5^{3x} + 32\cdot2^{3x} - 3125\cdot5^{3x} = 0, \\ (128+32)\cdot2^{3x} + (625-3125)\cdot5^{3x} = 0, \\ 160\cdot2^{3x} - 2500\cdot5^{3x} = 0, \\ 160\cdot2^{3x}} - 2500\cdot5^{3x} = 0, \\ 160\cdot\frac{2^{3x}}{5^{3x}} - 2500 = 0, \\ 160\cdot(\frac{2}{5})^{3x} = 2500, \\ (\frac{2}{5})^{3x} = \frac{2500}{160}, \\ (\frac{2}{5})^{3x} = \frac{125}{8},[/tex]
[tex](\frac{2}{5})^{3x} = (\frac{2}{5})^{-3}, \\ 3x=-3, \\ x=-1.[/tex]
