To solve this equation, first use the properties of logarithms to combine the terms on both sides of the equation.

lg(3x-7) + lg(2) = lg(x+3) + lg(x-3)
lg(2(3x-7)) = lg((x+3)(x-3))

Now apply the properties of logarithms to simplify the equation further:

lg(6x - 14) = lg(x^2 - 9)

Since the logarithms on both sides are equal, the expressions inside the logarithms must also be equal:

6x - 14 = x^2 - 9

Rearrange the equation into a quadratic form:

x^2 - 6x - 5 = 0

Now, we can factor the quadratic equation or use the quadratic formula to solve for x.