To solve the equation -7(3x-5)+2(7x-14)=28, we will first simplify both sides of the equation.

Starting with the left side:
-7(3x-5)+2(7x-14)
Distribute -7 and 2 to the terms inside the parentheses:
-21x + 35 + 14x - 28

Combining like terms:
-21x + 14x + 35 - 28
-7x + 7

Now, the equation becomes:
-7x + 7 = 28

To isolate the variable x, we will subtract 7 from both sides of the equation:
-7x + 7 - 7 = 28 - 7
-7x = 21

Finally, we will divide both sides of the equation by -7 to solve for x:
(-7x)/-7 = 21/-7
x = -3

Therefore, the solution to the equation -7(3x-5)+2(7x-14)=28 is x = -3.