If 3 times a square of an integer is added to 1 times the integer, the result is 2

Let unknown integer be n.

So then your sentence would translate to 3n² + n = 2.

If you need to solve for n then we can move 2 to left side by subtract both sides by 2:

3n² + n - 2 = 0

Now you can factor:

3n² + 3n - 2n - 2 = 0

3n (n + 1) - 2 (n + 1) = 0

(3n - 2) (n + 1) = 0

3n - 2 = 0 OR n + 1 = 0

3n = 2 OR n = - 1

n = 2/3 OR n = - 1

Final answer: n = 2/3 OR n = - 1