Let's simplify the given equation step by step:

15x - 7x(2x+5) = 4x(x+1)

15x - 14x^2 - 35x = 4x^2 + 4x

Combine like terms on both sides:

15x - 14x^2 - 35x = 4x^2 + 4x
15x - 14x^2 - 35x - 4x^2 - 4x = 0
-18x^2 - 24x = 0

Divide both sides by -6x to simplify:

-18x^2 - 24x = 0
-6x(3x + 4) = 0

Now, the equation simplifies to:

3x + 4 = 0

Solving for x, we get:

3x = -4
x = -4/3

Therefore, the solution to the equation is x = -4/3.