Question

The product of some negative number and 10 less than three times that number is 8

Answer 1

So,

"The product of some negative number"
n *

"and 10 less than three times that number"
-10 + 3n or 3n - 10

"is 8"
= 8
n * (3n - 10) = 8
n(3n - 10) = 8

Distribute.

`3n^2 - 10n = 8`

Subtract 8 from both sides.

`3n^2 - 10n - 8 = 0`

Factor.

`(3n + 2)(n - 4) = 0`

Set each factor to zero.
3n + 2 = 0
n - 4 = 0

There are two apparent solutions, but we must remember that the problem says that the number is negative. We must therefore discard the second equation as extraneous.

3n + 2 = 0

Subtract 2 from both sides.
3n = -2

Divide both sides by 3.

`n = (-2)/(3)`