Question

How do you solve `(x-4) (x-3)=0`?

Answer 1

`x=3" or "x=4`

Explanation:

Anything multiplied by zero gives the answer of zero.

So either of the brackets contents = 0

Thus we have

`x-4=0" "=>" "x=+4`

or

`x-3=0" "=>" "x=+3`

Answer 2

`x = 4 or x = 3`

Explanation:

If `axxbxxcxxd = 0" "` then we know for sure that at least one of the factors a, b, c, or d, MUST be equal to 0.

One of the properties of zero is that "Anything times 0 is equal to 0"

So, `a = 0, or b=0, or c=0, or d=0.`

To have a 0 from multiplying means we must start with a 0.

In `(x-4)(x-3)=0" "` we have the product of two factors equal to 0, ONE of them MUST be 0.

If `x-4 = 0" "rArr x = 4`

If `x-3 = 0" "rArr x = 3`

These are the two solutions.