SOLUTION: (4/(x+2)) + 3 = (3x/(x-3)) I do not need to graph, I just need to solve the equation (A rational equation, involving factoring and LCDs) and I am having some problems. The steps

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Question 160004: (4/(x+2)) + 3 = (3x/(x-3))
I do not need to graph, I just need to solve the equation (A rational equation, involving factoring and LCDs) and I am having some problems. The steps that I have are listed below:
4(x-3) + 3(x+2)(x+3) = 3x(x+2)
(4x-12)(3x+6)(3x-9) = 3x^2 + 6x
10x - 15 = 3x^2 + 6x
0 = 3x^2 - 4x + 15
I'm not sure if I did this problem correctly but I cannot seem to factor this equation for the correct answer.

Answer by KnightOwlTutor(293) (Show Source):
You can put this solution on YOUR website!
4(x-3) + 3(x+2)(x+3) = 3x(x+2) Sorry this is wrong (x+3) should be(x-3)
4(x-3)+3(x+2)(x-3)=3x(x+2)
4x-12 +3(x^2+2x-3x-6)=3x^2+6X
Simplify
4x-12+3(x^2-x-6)=3x^2+6x
4x-12+3x^2-3x-18=3x^2+6x
x-12-18+3x^2=3x^2+6x
x-30+3x^2=3x^2+6x
subtract 3x^2 from both sides
x-30=6x
subtract x from both sides
-30=5x
-6=x
Check answer by replacing x with -6 in the above equation
-6-6/-6-3=2(-6)/-6-3
-12/-9=-12/-9