The product of some negative number and 4 less than twice that number is 240. find the number.

Let the number be x

x(2x - 4) = 240
2x^2 - 4x = 240 Divide by 2
x^2 - 2x = 120
x^2 - 2x - 120 = 0
(x - 12)(x + 10) = 0

You want the negative number so 
x + 10 = 0 will give you a minus result.
x = - 10

Check the result
- 10 * ( 2*(-10) - 4) =? 240
- 10 * (- 24) = 240
240 = 240 so it check.

Notice that x = 12 also works, but 12 is not negative. Check this if you have the interest.

Ask google i believe they can you with that question