Answer
$x=${$-3- i\sqrt 3,-3+i\sqrt 3$}
Work Step by Step
Given: $x(x+6)=-12$
Re-write the given equation as: $x^2+6x=-12$
This implies that $x^2+6x+12=0$
Factorize the expression with the help of quadratic formula. Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
This implies that $x=\dfrac{-(6) \pm \sqrt{(6)^2-4(1)(12)}}{2(1)}$
or, $x=\dfrac{-6 \pm \sqrt {-12}}{2}$
or, $x=${$\dfrac{-6- 2i\sqrt 3}{2},\dfrac{-6+ 2i\sqrt 3}{2}$}
Hence, our solution set is: $x=${$-3- i\sqrt 3,-3+i\sqrt 3$}
