Question

The product of some negative number and 4 less than twice that number is 286 find the number

Answer 1

Let's say that number is hmmm "a"

now.. twice "a" is 2*a or 2a
4 less than that is " 2a - 4"

now, the product of those two fellows is 286, well ok

a( 2a - 4) = 286

thus    

$\bf a(2a-4)=286\implies 2a^2-4a^2=286\implies a^2-2a^2=143 \\\\\\ a^2-2a^2-143=0\implies (a-13)(a+11)=0 \\\\\\ \begin{cases} a-13=0\implies &a=13\\ a+11=0\implies &\boxed{a=-11} \end{cases}$