Let's start by simplifying the left side of the equation:

3x(x+1) - 2x(5x+3) < 7x(2-x) + 4

Expand the terms:
3x^2 + 3x - 10x^2 - 6x < 14x - 7x^2 + 4

Combine like terms:
-7x^2 - 3x < 14x - 7x^2 + 4

Now, we can simplify further by eliminating the -7x^2 terms on both sides:

-3x < 14x + 4

Now, we want to isolate the variable x by adding 3x to both sides:

0 < 17x + 4

Then, we subtract 4 from both sides:

-4 < 17x

Finally, divide by 17 on both sides to solve for x:

-4/17 < x

Therefore, the solution to the inequality 3x(x+1) - 2x(5x+3) < 7x(2-x) + 4 is x > -4/17.