4 / (z + 3) = 2 / (z - 2)
So multiply both sides by (z + 3) and (z - 2), then you get:
4(z - 2) = 2(z + 3)
Now multiply out the brackets:
4(z - 2) = 2(z + 3)
=> 4z - 8 = 2z + 6
Now subtract '2z' from both sides of the equation to get all the 'z' terms on the same side:
So, 4z - 8 = 2z + 6 becomes
4z - 2z - 8 = 2z - 2z + 6
=> 2z - 8 = 6
Now add 8 to both sides of the equation:
So, 2z - 8 = 6 becomes
2z - 8 + 8 = 6 + 8
=> 2z = 14
Now divide through by 2 to find the value of z:
(2z)/2 = 14/2
=> z = 7
So the solution is z = 7.