# SOLUTION: Solve the following equation (2x^2+x+1)(2x^2+x+2)=12 using a substitution

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 Question 27647: Solve the following equation (2x^2+x+1)(2x^2+x+2)=12 using a substitutionAnswer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!Solve the following equation (2x^2+x+1)(2x^2+x+2)=12 using a substituton LET 2X^2+X=Y..HENCE WE HAVE (Y+1)(Y+2)=12 Y^2+3Y+2-12=0 Y^2+3Y-10=0 (Y+5)(Y-2)=0 Y=-5 OR 2 CASE1 2X^2+X=-5 2X^2+X+5=0 DISCRIMINANT IS NEGATIVE.ROOTS ARE IMAGINARY.ARE YOU ARE TAUGHT IMAGINARY NUMBERS?OTHERWISE SAY NO SOLUTION. CASE2 2X^2+X=2 2X^2+X-2=0 USING QUADRATIC FORMULA WE GET X={-1+SQRT17}/2 OR X={-1-SQRT17)/2