Explanation:

The given expression is,
a²+b²+c²=2(2a−3b−5c)−38
Or, (a−2)²+(b+3)²+(c+5)²=0, rearranging the terms and collecting suitable terms together, what we call principle of collection of friendly terms.
As each of the square expressions must be zero for their sum to be zero by principle of zero sum of square terms,
a−2=0,
Or, a=2.
Similarly,
b=−3, and
c=−5.
So,
a−b−c=10.