ok, but your second line should be technically
(x+6-sqrt13)(x+6+sqrt13)
[x-(-6+sqrt13)][x-(-6-sqrt13)]
(x+6+sqrt13)(x+6-sqrt13)
(x+6+sqrt13)(x+6+sqrt13)
(x^2+12x+36-sqrt13^2)
x^2+12x+36-sqrt13^2
x^2+12x+36-(13)
x^2+12x+36-13
I think my answer is:
x^2+12x+23
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