(3x^2+7x+4)*((x^2-4x)/(9x^2+12x))0

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Solution for (3x^2+7x+4)*((x^2-4x)/(9x^2+12x))0 equation: 


D( x )

(x^2-(4*x))/(9*x^2+12*x) = 0

9*x^2+12*x = 0

(x^2-(4*x))/(9*x^2+12*x) = 0

(x^2-(4*x))/(9*x^2+12*x) = 0

(x^2-4*x)/(9*x^2+12*x) = 0

x^2-4*x = 0

x*(x-4) = 0

x-4 = 0 // + 4

x = 4

x*(x-4) = 0

9*x^2+12*x = 0

3*x*(3*x+4) = 0

3*x+4 = 0 // - 4

3*x = -4 // : 3

x = -4/3

3*x*(x+4/3) = 0

(x*(x-4))/(3*x*(x+4/3)) = 0

( x-4 )

x-4 = 0 // + 4

x = 4

( x )

x = 0

9*x^2+12*x = 0

9*x^2+12*x = 0

9*x^2+12*x = 0

DELTA = 12^2-(0*4*9)

DELTA = 144

DELTA > 0

x = (144^(1/2)-12)/(2*9) or x = (-144^(1/2)-12)/(2*9)

x = 0 or x = -4/3

x in (-oo:-4/3) U (-4/3:0) U (0:4) U (4:+oo)

(3*x^2+7*x+4)*((x^2-(4*x))/(9*x^2+12*x))^0 = 0

3*x^2+7*x+4 = 0

3*x^2+7*x+4 = 0

DELTA = 7^2-(3*4*4)

DELTA = 1

DELTA > 0

x = (1^(1/2)-7)/(2*3) or x = (-1^(1/2)-7)/(2*3)

x = -1 or x = -4/3

x in { -4/3} 

x = -1

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