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

Using the property of logarithms that lg(a) - lg(b) = lg(a/b), we can simplify the equation as follows:

lg(2x^2 - 5x) = lg(15x - 42)
lg((2x^2 - 5x)/(15x - 42)) = 0

Since the logarithm of 0 is always 0, we can simplify further:

(2x^2 - 5x)/(15x - 42) = 1

Now, we can solve for x by cross multiplying:

2x^2 - 5x = 15x - 42
2x^2 - 20x + 42 = 0

Now, we can factor the quadratic equation:

(2x - 7)(x - 6) = 0

Setting each factor to zero and solving for x, we get:

2x - 7 = 0
2x = 7
x = 7/2

x - 6 = 0
x = 6

Therefore, the solutions to the equation lg(2x^2 - 5x) = lg(15x - 42) are x = 7/2 and x = 6.