Question

How do you solve (2z-3)(4z-7)=0

Answer 1

There are two values of z in this question. (2z - 3)
-3 / 2 = -1.5
-1.5 x -1 = 1.5

(4z - 7)
-7 / 4 = -1.75
-1.75 x -1 = 1.75

z = 1.5 or 1.75

Answer 2

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 .