To solve this system of equations, we can substitute xy=15 into the second equation to get rid of one variable:

x^2 + y^2 + x + y = 12
x^2 + y^2 + 15 + x + y = 12
x^2 + y^2 + x + y = -3

Now we have a new system of equations:

xy = 15
x^2 + y^2 + x + y = -3

We can now solve this system by substitution. Solving for y in the first equation, we get:

y = 15/x

Substitute this into the second equation:

x^2 + (15/x)^2 + x + 15/x = -3
x^2 + 225/x^2 + x + 15/x = -3
x^4 + 225 + x^3 + 15 = -3x^2
x^4 + x^3 + 3x^2 + 15 - 3 = 0

This is a quartic equation that can be solved by factoring or using numerical methods.