To solve this equation, we need to simplify both sides of the equation.

On the left side:
(3x - 2^4) x 7^3

First, simplify the exponent:
(3x - 16) x 343

On the right side:
2 x 7^4

Simplify the exponent:
2 x 2401

Now we have:
(3x - 16) x 343 = 2 x 2401

Next, simplify both sides of the equation:
1029x - 5488 = 4802

Now, isolate the variable by adding 5488 to both sides:
1029x = 10290

Finally, divide both sides by 1029 to solve for x:
x = 10