Question

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

Answer 1

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 .

Answer 2

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