### Instruction: Find all solutions to the equation $\sqrt{3x+6}=x+2$.  If there are multiple solutions, order them from least to greatest, separated by comma(s).### Response: To find the solutions to this equation, I will first try to isolate x on one side by squaring both sides.
This gives me:

$(\sqrt{3x+6})^2=(x+2)^2$
Simplifying, I get:

$3x+6=x^2+4x+4$
Rearranging the terms, I obtain a quadratic equation:

$x^2+x-2=0$
To solve this, I can either use the quadratic formula or factor the expression.
I notice that the expression can be factored as:

$(x+2)(x-1)=0$
Therefore, the possible solutions are x=-2 and x=1.
However, I have to check if these solutions satisfy the original equation, because sometimes squaring both sides can introduce extraneous solutions.
Plugging in x=-2, I get:

$\sqrt{3(-2)+6}=(-2)+2$

$\sqrt{0}=0$

$0=0$
This is true, so x=-2 is a valid solution.
Plugging in x=1, I get:

$\sqrt{3(1)+6}=(1)+2$

$\sqrt{9}=3$

$3=3$
This is also true, so x=1 is another valid solution.