Question

How do you solve `(4a - 7) ( 3a + 8) = 0`?

Answer 1

Since it is already factored, we can write the roots as `a=-8/3` or `a=7/4`

Explanation:

If either of the bracketed expressions gives zero, then clearly this is a root of the equation:

And if `4a-7=0`, then `a=7/4`, that's one root,

And if `3a+8=0`, then `a=-8/3` is the other root.

This would not be at all obvious if we were asked to find the roots of the expression:

`12a^2 +11a-56=0`