To solve this equation, first distribute the terms on both sides:

(x^2 + 1)(x - 2) - (x^2 + 3)(x - 1) + 7x - 1 = 0
x^3 - 2x^2 + x - 2 - (x^3 - x^2 + 3x - 3) + 7x - 1 = 0
x^3 - 2x^2 + x - 2 - x^3 + x^2 - 3x + 3 + 7x - 1 = 0
-2x^2 + x - 2 - 3x + 3 + 7x - 1 = 0
-2x^2 + 5x = 0

Now, factor out x:

x(-2x + 5) = 0

Setting each factor to zero gives:

x = 0 or -2x + 5 = 0
-2x = -5
x = 5/2

Therefore, the solutions to the equation are x = 0 and x = 5/2.