8/(x+6)=-3/(2x+12)+2

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Solution for 8/(x+6)=-3/(2x+12)+2 equation: 


D( x )

2*x+12 = 0

x+6 = 0

2*x+12 = 0

2*x+12 = 0

2*x+12 = 0 // - 12

2*x = -12 // : 2

x = -12/2

x = -6

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x in (-oo:-6) U (-6:+oo)

8/(x+6) = 2-3/(2*x+12) // - 2-3/(2*x+12)

8/(x+6)-(-3/(2*x+12))-2 = 0

8/(x+6)+3*(2*x+12)^-1-2 = 0

8/(x+6)+3/(2*x+12)-2 = 0

(8*(2*x+12))/((x+6)*(2*x+12))+(3*(x+6))/((x+6)*(2*x+12))+(-2*(x+6)*(2*x+12))/((x+6)*(2*x+12)) = 0

8*(2*x+12)+3*(x+6)-2*(x+6)*(2*x+12) = 0

19*x-4*x^2-48*x-144+114 = 0

-4*x^2-29*x-30 = 0

-4*x^2-29*x-30 = 0

-1*(4*x^2+29*x+30) = 0

4*x^2+29*x+30 = 0

DELTA = 29^2-(4*4*30)

DELTA = 361

DELTA > 0

x = (361^(1/2)-29)/(2*4) or x = (-361^(1/2)-29)/(2*4)

x = -5/4 or x = -6

-1*(x+6)*(x+5/4) = 0

(-1*(x+6)*(x+5/4))/((x+6)*(2*x+12)) = 0

(-1*(x+6)*(x+5/4))/((x+6)*(2*x+12)) = 0 // * (x+6)*(2*x+12)

-1*(x+6)*(x+5/4) = 0

( x+5/4 )

x+5/4 = 0 // - 5/4

x = -5/4

( x+6 )

x+6 = 0 // - 6

x = -6

x in { -6} 

x = -5/4

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