Question 1204189
<pre>
Let the middle integer be x, then the first one is x-1 and the third one is x+1.

x-1 = smallest
x = middle
x+1 = largest

The product of the first and third of three negative consecutive integers 

That's (x-1)(x+1)

is 59 more than 4 times the second integer. Find the integers.

That's 4x + 59

(x-1)(x+1) = 4x + 59

x2 - 1 = 4x + 59
x2 - 4x - 60 = 0
(x + 6)(x - 10) = 0
x + 6 = 0;  x - 10 = 0
    x = -6;      x = 10

We are told that the integers are negative, so we discard x=10

x-1 = smallest = -6-1 = -7
x = middle     = -6  
x+1 = largest  = -6+1 = -5

Checking the words:

The product of the first and third...

(-7)(-5) = 35

...is 59 more than 4 times the second integer. 

That's 59 more than 4 times -6, which is -24.  Sure enough,'
it's true that (-24) + 59 = 35.

Edwin</pre>