2/(4x+7)+x/3=6/(12x+21)

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Solution for 2/(4x+7)+x/3=6/(12x+21) equation: 


D( x )

12*x+21 = 0

4*x+7 = 0

12*x+21 = 0

12*x+21 = 0

12*x+21 = 0 // - 21

12*x = -21 // : 12

x = -21/12

x = -7/4

4*x+7 = 0

4*x+7 = 0

4*x+7 = 0 // - 7

4*x = -7 // : 4

x = -7/4

x in (-oo:-7/4) U (-7/4:+oo)

2/(4*x+7)+x/3 = 6/(12*x+21) // - 6/(12*x+21)

2/(4*x+7)-(6/(12*x+21))+x/3 = 0

2/(4*x+7)-6*(12*x+21)^-1+x/3 = 0

2/(4*x+7)-6/(12*x+21)+x/3 = 0

(2*3*(12*x+21))/(3*(4*x+7)*(12*x+21))+(-6*3*(4*x+7))/(3*(4*x+7)*(12*x+21))+(x*(4*x+7)*(12*x+21))/(3*(4*x+7)*(12*x+21)) = 0

2*3*(12*x+21)-6*3*(4*x+7)+x*(4*x+7)*(12*x+21) = 0

48*x^3+168*x^2+147*x = 0

48*x^3+168*x^2+147*x = 0

3*x*(16*x^2+56*x+49) = 0

16*x^2+56*x+49 = 0

DELTA = 56^2-(4*16*49)

DELTA = 0

x = -56/(2*16)

x = -7/4 or x = -7/4

3*x*(x+7/4)^2 = 0

(3*x*(x+7/4)^2)/(3*(4*x+7)*(12*x+21)) = 0

(3*x*(x+7/4)^2)/(3*(4*x+7)*(12*x+21)) = 0 // * 3*(4*x+7)*(12*x+21)

3*x*(x+7/4)^2 = 0

( 3*x )

3*x = 0 // : 3

x = 0

( x+7/4 )

x+7/4 = 0 // - 7/4

x = -7/4

x in { -7/4} 

x = 0

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