To solve the equation 8x(5-3x) - 5 + 3x = 0, we can start by simplifying the expression:

8x(5-3x) - 5 + 3x = 0
40x - 24x^2 - 5 + 3x = 0

Next, we can combine like terms:

40x + 3x - 24x^2 - 5 = 0
43x - 24x^2 - 5 = 0

Now, we can rearrange the equation to form a quadratic equation:

-24x^2 + 43x - 5 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring may not be straightforward, so we'll use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = -24, b = 43, and c = -5. Plugging these values into the quadratic formula, we get:

x = (-43 ± √(43^2 - 4(-24)(-5))) / (2(-24))
x = (-43 ± √(1849 - 480)) / (-48)
x = (-43 ± √1369) / (-48)

Now, we can simplify the square root:

x = (-43 ± 37) / (-48)

This gives us two possible solutions:

x = (-43 + 37) / (-48) = -6 / (-48) = 1/8
x = (-43 - 37) / (-48) = -80 / (-48) = 5/3

Therefore, the solutions to the equation 8x(5-3x) - 5 + 3x = 0 are x = 1/8 and x = 5/3.