Let's solve this equation step by step.

Firstly, we will simplify the left side of the equation:
3*(2x-5)-4x
= 6x - 15 - 4x
= 2x - 15

Next, we simplify the right side of the equation:
5(x-9) + 277(x-5) - 3(1-2x)
= 5x - 45 + 277x - 1385 - 3 + 6x
= 288x - 1433

Finally, we simplify the last part of the equation:
16 - 3(2x-1)
= 16 - 6x + 3
= 19 - 6x

Now, putting it all together, we get:
2x - 15 = 288x - 1433 = 19 - 6x

Combining like terms on the right side, we get:
2x - 15 = 282x - 1414

Now, let's isolate x:
2x - 282x = 1414 + 15
-280x = 1429
x = -1429 / 280
x ≈ -5.103

Therefore, the solution to the equation is x ≈ -5.103.