SOLUTION: sqrt(5x+6)-sqrt(3x-2)=2 solve for x. please show all the steps involved. thanks!

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Question 6739: sqrt(5x+6)-sqrt(3x-2)=2 solve for x.
please show all the steps involved. thanks!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
sqrt%285x%2B6%29-sqrt%283x-2%29+=+2 Add sqrt%283x-2%29 to both sides.
sqrt%285x%2B6%29+=+2+%2B+sqrt%283x-2%29 Square both sides.
%285x%2B6%29+=+4+%2B+4sqrt%283x-2%29+%2B+%283x-2%29 Simplify.
5x%2B6+=+2+%2B+3x+%2B+4sqrt%283x-2%29 Subtract 3x from both sides.
2x%2B6+=+2+%2B+4sqrt%283x-2%29 Subtract 2 from both sides.
2x%2B4+=+4sqrt%283x-2%29 Square both sides.
4x%5E2+%2B+16x+%2B+16+=+16%283x-2%29 Simplify.
4x%5E2+%2B+16x+%2B+16+=+48x+-+32 Subtract 48x from both sides.
4x%5E2+-+32x+%2B+16+=+-32 Add 32 to both sides.
4x%5E2+-+32x+%2B+48+=+0 Divide both sides by 4.
x%5E2+-+8x+%2B+12+=+0 Solve by factoring.
%28x+-+2%29%28x+-+6%29+=+0 Apply the zero product principle.
x - 2 = 0, x = 2 or
x - 6 = 0, x = 6