To solve this equation, first distribute the terms on the right side of the equation:

X(x-3) = 4(x+1) + 3x^2 - 7x
X^2 - 3X = 4X + 4 + 3X^2 - 7X

Now, combine like terms:

X^2 - 3X = 4X + 4 + 3X^2 - 7X
X^2 - 3X = X^2 - 3X + 4

Since the X^2 and -3X terms cancel out, we are left with:

0 = 4

This equation is not true, which means that there is no solution to the original equation X(x-3) = 4(x+1) + 3x^2 - 7x.