Question

How do you solve `x^2 - 21x - 72 = 0`?

Answer 1

this quadratic equation can be factored as `(x-24)(x+3)=0`

now that we have a product of two factors equal to zero, that means that at least one of the factors MUST be equal to zero.
so

we have `x-24=0 or x+3=0`
this means that we have now reduced this to a matter of solving 2 linear equations.
and `x=24 or x=-3` are two different solutions for x

Answer 2

-3 and 24

Explanation:

`y = x^2 - 21x - 72 = 0`
Use the new Transforming Method (Google, Yahoo Search).
The 2 real roots have opposite signs because ac < 0.
Compose factor pairs of (-72) --> (-2, 36)(-3, 24). This last sum is
(24 - 3) = 21 = -b. Then, the 2 real roots are: -3 and 24.

NOTE
There is no need to factor by grouping and solving the 2 binomials.