Step 1: Set this expression equal to 0. We get
-2x2+19x-24 = 0
What we want is to do is use the
quadratic formula to solve for the
roots of the equation.
a = -2,
b = 19, and
c = -24. Plugging these numbers into the
quadratic formula we get:
One root is (-19-13)/-4 = 8.
The other root is (-19+13)/-4 = 3/2. We
(x-8)(-2x +3) = 0
because we want the first term of our expanded FOIL expression to
multiply to -2x2.
So -2x2+19x-24 = (x-8)(-2x +3).