(3/(2w+12))+4=-(4/(w+6))

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Solution for (3/(2w+12))+4=-(4/(w+6)) equation: 


D( w )

w+6 = 0

2*w+12 = 0

w+6 = 0

w+6 = 0

w+6 = 0 // - 6

w = -6

2*w+12 = 0

2*w+12 = 0

2*w+12 = 0 // - 12

2*w = -12 // : 2

w = -12/2

w = -6

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

3/(2*w+12)+4 = -(4/(w+6)) // + 4/(w+6)

3/(2*w+12)+4/(w+6)+4 = 0

(3*(w+6))/((2*w+12)*(w+6))+(4*(2*w+12))/((2*w+12)*(w+6))+(4*(2*w+12)*(w+6))/((2*w+12)*(w+6)) = 0

3*(w+6)+4*(2*w+12)+4*(2*w+12)*(w+6) = 0

8*w^2+11*w+96*w+66+288 = 0

8*w^2+107*w+354 = 0

8*w^2+107*w+354 = 0

8*w^2+107*w+354 = 0

DELTA = 107^2-(4*8*354)

DELTA = 121

DELTA > 0

w = (121^(1/2)-107)/(2*8) or w = (-121^(1/2)-107)/(2*8)

w = -6 or w = -59/8

(w+59/8)*(w+6) = 0

((w+59/8)*(w+6))/((2*w+12)*(w+6)) = 0

((w+59/8)*(w+6))/((2*w+12)*(w+6)) = 0 // * (2*w+12)*(w+6)

(w+59/8)*(w+6) = 0

( w+59/8 )

w+59/8 = 0 // - 59/8

w = -59/8

( w+6 )

w+6 = 0 // - 6

w = -6

w in { -6} 

w = -59/8

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