Question

How do you use algebra to solve `(x-1)(x+2)=18`?

Answer 1

We know that a if a product is `0`, then at least one of the factors must be `0`. But, that's not what we have here.

Let's try to make it what we have:

`(x-1)(x+2)=18`
`(x-1)(x+2)-18=0`

Great!, Except -- now we don't have a product on the left. Try something and see if it helps or makes things worse.
(I have experience, I often know what will work. A less experienced person has to just try something.)

`[x^2+x-2] - 18 =0` (I multiplied `(x-1)(x+2)`)

`x^2+x-20=0` (Simplify)
`(x+5)(x-4)=0` (Factor the NEW expression)

`x+5=0` or `x-4=0`

It is clear that there are 2 solutions: `-5` is a solution and `4` is a solution