Answer
$\{-6,-3,3\}$
Work Step by Step
Taking the positive:
$$x^2+6x=3x+18$$
$$x^2+3x-18=0$$
$$(x+6)(x-3)=0$$
$$x+6=0$$
$$x=-6$$
$$x-3=0$$
$$x=3$$
Checking:
For $x=-6$:
$$|(-6)^2+6(-6)|=3(-6)+18$$
$$0=0~True$$
Thus, $x=-6$ is a solution.
For $x=3$:
$$|(3^2+6(3)|=3(3)+18$$
$$27=27~True$$
Thus, $x=3$ is a solution.
Taking the negative:
$$x^2+6x=-(3x+18)$$
$$x^2+6x=-3x-18$$
$$x^2+9x+18=0$$
$$(x+6)(x+3)=0$$
$$x+6=0$$
$$x=-6$$
$$x+3=0$$
$$x=-3$$
Checking for $x=-3$:
$$|((-3)^2+6(-3)|=3(-3)+18$$
$$9=9~True$$
Thus, $x=-3$ is a solution.
Therefore, the solution is:
$$x=-6,-3,3$$
