Question

How do you solve `(b + 3) ( b - 6) = 0`?

Answer 1

`color(blue)(b=-3), color(red) (b=6)`

Explanation:

Set up two equations and solve

`color(blue)(b+3=0)`
`color(blue)(b+cancel3cancel(-3)=0-3`
`color(blue)(b=-3)`

`color(red)(b-6=0)`
`color(red)(b-cancel6cancel(+6)=0+6`
`color(red)(b=6)`

Answer 2

b = -3, 6

Explanation:

You have to find the values of b that makes the equation `(b+3)(b-6) = 0` true.

If you can make one of the results of the parentheses equal to 0, then you know that automatically the whole equation would have a result of 0. In other words, if we can find the value of b that makes `(b+3) = 0`, then if we multiply `0(b-6)`, we can automatically get the product of 0. We can apply the same concept to the other set of parentheses.

A number added to its opposite will equal to 0, and in the case of `b+3`, we know that `-3 +3` will equal to 0. Therefore one value of b could be -3.
`(-3 + 3)(b-6) = 0`
`0(b-6) = 0`
`0 = 0`

As for `b-6` equaling to 0, we know that `6-6` equals to 0. Therefore, b can also equal to 6.
`(b + 3)(6-6) = 0`
`(b+3)0 = 0`
`0 = 0`