Question

Solve the equation using the zero-product property (2x-8)(7x+5)=0

Answer 1

x = 4 and x = -5/7

Explanation:

The zero product property states that if ab =0, then a =0 or b = 0 or both a and b equal to zero.

We are given (2x - 8)(7x + 5) = 0

Using the property, we can write it as

(2x - 8) = 0 or (7x + 5) = 0

Now we have to solve for x.

Let's solve the first one.

2x - 8 = 0

Add 8 on both sides, we get

2x - 8 + 8 = 8

2x = 8

Dividing both sides by 2, we get

2x/2 = 8/2

x = 4

Now let's solve the second one.

7x + 5 =0

Subtract 5 on both sides, we get

7x = -5

Dividing both sides by 7, we get

x = -5/7

Therefore, the solutions are x = 4 and x = -5/7

Answer 2

if xy=0 assume that x and y=0
so
(2x-8)(7x+5)=0
assume
2x-8=0 and 7x+5=0
solve each

2x-8=0
2x=8
x=4

7x+5=0
7x=-5
x=-5/7

so x=-5/7 or 4