how many solutions does −5(z+1)=−2z+10 have

Answer 1

It can have at most one solution. You did not ask for a solution, but I assume that was the real intent of this question.

-5(z + 1) = -2z + 10

-5z - 5 = -2z + 10

-3z = 15

z = -5

Answer 2

-5z + -5 = -2z + 10

-5 = 3z + 10

-15 = 3z

z = -5

one solution and it checks