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.
\(n = \frac{-2}{3}\)
