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Question

Solve the following for x:
12a+b+2x=12a+1b+12x

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Solution

12a+b+2x=12a+1b+12x

12a+b+2x+12x=2a+b2ab

2x+2a+b+2x2x.(2a+b+2x)=2a+b2ab

2a+b+4x2ax+bx+2x2=2a+bab

2a2b+ab2+4abx=4a2+2abx+4ax2+2abx+b2x+2bx2

2a2b+ab2=x2(4a+2b)+x(4a2+b2)

x=±[(4a2+b2)+(4a2+b2)2+4(4a+2b)(2a2b+ab2)2(4a+2b)]

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