The key to this is to realize that if EITHER quantity in parentheses is zero,
then the whole left side is zero, and the equation is true.
First quantity: (2z-3). If this is zero, then the whole equation is true.
2z - 3 = 0
Add 3 to each side: 2z = 3
Divide each side by 2: z = 3/2 or 1.5
Second quantity: (4z-7). If this is zero, then the whole equation is true.
4z - 7 = 0
Add 7 to each side: 4z = 7
Divide each side by 4: z = 7/4 or 1.75
So the original equation has two solutions:
z = 1.5
and
z = 1.75 .
