Let's start by expanding both sides of the equation:

(5x - 7) x = (x - 3) (4x - 3)

Expanding the left side:
5x^2 - 7x = 4x^2 - 3x - 12x + 9
5x^2 - 7x = 4x^2 - 15x + 9

Now, let's combine like terms and simplify the equation:
5x^2 - 7x = 4x^2 - 15x + 9
5x^2 - 7x - 4x^2 + 15x - 9 = 0
x^2 + 8x - 9 = 0

Now, let's factor the quadratic equation:
(x + 9)(x - 1) = 0

Setting each factor to zero:
x + 9 = 0 or x - 1 = 0

Solving for x:
x = -9 or x = 1

Therefore, the solutions to the equation are x = -9 and x = 1.