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I have an equation y = -2x - 2

I have tried the following but am struggling with the final understanding.

(x + 3)^2 + (y - 4)^2 = 5

(x + 3)^2 = x^2 + 6x +9

(y - 4)^2 = 4x^2 + 24x + 36

combining and cancelling gives

5x^2 + 30x + 39 = 0

I now require to find the factors, which I am struggling with, I am thinking

x^2 + 10x + 13

In my head I have these numbers running round, factors 3, 6 and 5. I know there is a method to working this out like 3 x 13 = 39, and 6 x 5 = 30 etc, but I just can't seem to grasp it?

Any help appreciated

Thanks