To find a^2 + b^2 + c^2, we need to find the values of a, b, and c first.

From the equations given:
a + b + c = 12
ab + ac + bc = -15

Now, let's square the equation a + b + c = 12:
(a + b + c)^2 = 12^2
a^2 + b^2 + c^2 + 2(ab + ac + bc) = 144
a^2 + b^2 + c^2 + 2(-15) = 144
a^2 + b^2 + c^2 - 30 = 144
a^2 + b^2 + c^2 = 174

Therefore, a^2 + b^2 + c^2 = 174.