(z^2+12z+27)/(z^2+13z+36)*(z^2+6z+8)/(z^2+32)

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Solution for (z^2+12z+27)/(z^2+13z+36)*(z^2+6z+8)/(z^2+32) equation: 


D( z )

z^2+32 = 0

z^2+13*z+36 = 0

z^2+32 = 0

z^2+32 = 0

1*z^2 = -32 // : 1

z^2 = -32

z^2+13*z+36 = 0

z^2+13*z+36 = 0

z^2+13*z+36 = 0

DELTA = 13^2-(1*4*36)

DELTA = 25

DELTA > 0

z = (25^(1/2)-13)/(1*2) or z = (-25^(1/2)-13)/(1*2)

z = -4 or z = -9

z in (-oo:-9) U (-9:-4) U (-4:+oo)

(((z^2+12*z+27)/(z^2+13*z+36))*(z^2+6*z+8))/(z^2+32) = 0

((z^2+12*z+27)*(z^2+6*z+8))/((z^2+13*z+36)*(z^2+32)) = 0

z^2+12*z+27 = 0

z^2+12*z+27 = 0

DELTA = 12^2-(1*4*27)

DELTA = 36

DELTA > 0

z = (36^(1/2)-12)/(1*2) or z = (-36^(1/2)-12)/(1*2)

z = -3 or z = -9

(z+9)*(z+3) = 0

z^2+13*z+36 = 0

z^2+13*z+36 = 0

DELTA = 13^2-(1*4*36)

DELTA = 25

DELTA > 0

z = (25^(1/2)-13)/(1*2) or z = (-25^(1/2)-13)/(1*2)

z = -4 or z = -9

(z+9)*(z+4) = 0

z^2+6*z+8 = 0

z^2+6*z+8 = 0

DELTA = 6^2-(1*4*8)

DELTA = 4

DELTA > 0

z = (4^(1/2)-6)/(1*2) or z = (-4^(1/2)-6)/(1*2)

z = -2 or z = -4

(z+4)*(z+2) = 0

((z+9)*(z+3)*(z+4)*(z+2))/((z+9)*(z+4)*(z^2+32)) = 0

( z+2 )

z+2 = 0 // - 2

z = -2

( z+3 )

z+3 = 0 // - 3

z = -3

( z+4 )

z+4 = 0 // - 4

z = -4

( z+9 )

z+9 = 0 // - 9

z = -9

z in { -4} 

z in { -9} 

z in { -2, -3 }

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