Given the equation -4a/a+4=12/a-11, for sure we need to the solution for a.
-4a/a+4=12/a-11
-3a + 4 = 12/a - 11
-3a -12/a = -11 - 4
3a + 12 / a = 15
(3a^2 + 12) / a = 15
3a^2 + 12 = 15a
3a^2 - 15a + 12 = 0
In order to get a , we need to find the roots.
(3a - 3) (a - 4) = 0
3a - 3 = 0 --> a = 1
a - 4 = 0 -- > a = 4
So the possible solutions for a are 1 and 4.