SOLUTION: Any help at all with this equation would be greatly appreciated. Solve. 3x(x+3) = 2(5x +1)

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Question 304581: Any help at all with this equation would be greatly appreciated.
Solve. 3x(x+3) = 2(5x +1)
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: 3X%2A%28X+%2B+3%29+=+2%2A%285X+%2B+1%29
Multiply both sides through
3X%5E2+%2B+9X+=+10X+%2B+2 Move everything to one side
3X%5E2+%2B+9X+-+10X+-+2+=+0 Simplify
3X%5E2+-+X+-+2+=+0
Find the factors of 2: They are only 1 and 2
(If you do not see how to unfoil the equation you could use the quadratic equation.)
Unfoil the equation.
%283X+%2B+2%29%2A%28X+-+1%29+=+0
Set each portion to 0
3X+%2B+2+=+0
3X+=+-2
highlight%28X+=+-2%2F3%29
-------------------------
X+-+1+=+0
highlight_green%28X+=+1%29
------------------------------
Here is the quadratic equation way......
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-1x%2B-2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A3%2A-2=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+25+%29%29%2F2%5C3+=+1
x%5B2%5D+=+%28-%28-1%29-sqrt%28+25+%29%29%2F2%5C3+=+-0.666666666666667

Quadratic expression 3x%5E2%2B-1x%2B-2 can be factored:
3x%5E2%2B-1x%2B-2+=+3%28x-1%29%2A%28x--0.666666666666667%29
Again, the answer is: 1, -0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-1%2Ax%2B-2+%29