(x^2+x+3)^2+12x^2+12x-9=0

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To solve this equation, first expand the terms inside the parentheses:

(x^2 + x + 3)^2 = x^4 + 2x^3 + 9x^2 + 2x^2 + 6x + 9
= x^4 + 2x^3 + 11x^2 + 6x + 9

Now the equation becomes:

x^4 + 2x^3 + 11x^2 + 6x + 9 + 12x^2 + 12x - 9 = 0
x^4 + 2x^3 + 23x^2 + 18x = 0

Now factor out an x:

x(x^3 + 2x^2 + 23x + 18) = 0

Now we can solve for x by setting each factor to zero:

x = 0

To solve the cubic equation x^3 + 2x^2 + 23x + 18 = 0, we can use numerical methods or factor it into linear and quadratic factors.