To solve the equation (2x-3)-(-4x+1)=2×(-5), we can start by simplifying both sides of the equation.

First, let's simplify the left side:

(2x-3)-(-4x+1)

Distribute the negative sign to the terms inside the parentheses:

2x - 3 + 4x - 1

Combine like terms:

(2x + 4x) + (-3 - 1)

6x - 4

Now let's simplify the right side:

2×(-5)

-10

Now we have the equation:

6x - 4 = -10

To solve for x, we can isolate the variable by adding 4 to both sides:

6x - 4 + 4 = -10 + 4

6x = -6

Finally, divide both sides by 6 to solve for x:

6x/6 = -6/6

x = -1

Therefore, the solution to the equation (2x-3)-(-4x+1)=2×(-5) is x = -1.