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This is an advanced quadratic equation.  Solve for x.

 

 Jul 3, 2020
 #1
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Solve:       ( x2 + x + 1 ) ( x2 + x + 2 )  =  12

Multiply out:  x4 + 2x3 + 4x2 + 3x + 2  =  12

Rewrite:       x4 + 2x3 + 4x2 + 3x - 10  =  0

 

There are two rational solutions; you can find them by trying all the factors of -10:

     1, -1, 2, -2, 5, -5, 10, -10          (two of these will work)

 

After you have these two solutions, you can divide their factors out of the original problem.

This will give you a quadratic that can be solved by using the quadratic equation.

 Jul 3, 2020

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