To solve the equation 5x−2(2x−7)=2(3x−1)+72, we will follow these steps:

Step 1: Distribute the terms
First, we will distribute the terms on both sides of the equation.

5x−2(2x−7)=2(3x−1)+72

Distributing on the left side:
5x−4x+14

Distributing on the right side:
6x−2+72

So, the equation now looks like:
5x−4x+14=6x−2+72

Step 2: Simplify both sides
Now, simplify both sides of the equation:
x+14=6x−2+72

Step 3: Combine like terms
Next, we will combine the constants on the right side. To do this, we need to convert −2 into a fraction with a denominator of 2:
−2=−42

So, we can rewrite the right side:
x+14=6x−42+72=6x+32

Step 4: Move all terms involving x to one side
Now, we will move all x terms to one side by subtracting x from both sides:
14=6x−x+32
14=5x+32

Step 5: Isolate the x term
Next, we will isolate the x term by subtracting 32 from both sides. To do this, we convert 14 into a fraction:
14=282
So,
282−32=5x
252=5x

Step 6: Solve for x
Now, we will divide both sides by 5 to solve for x:
x=252÷5=252×15=2510=52

Thus, the solution is:
x=2.5