(((z^2)+7z+12)/(z+1))(((z^2)-2z-3)/(z+3))

Solution for (((z^2)+7z+12)/(z+1))(((z^2)-2z-3)/(z+3)) equation:

D( z )

z+1 = 0

z+3 = 0

z+1 = 0

z+1 = 0

z+1 = 0 // - 1

z = -1

z+3 = 0

z+3 = 0

z+3 = 0 // - 3

z = -3

z in (-oo:-3) U (-3:-1) U (-1:+oo)

((z^2+7*z+12)/(z+1))*((z^2-(2*z)-3)/(z+3)) = 0

((z^2+7*z+12)/(z+1))*((z^2-2*z-3)/(z+3)) = 0

((z^2+7*z+12)*(z^2-2*z-3))/((z+1)*(z+3)) = 0

z^2+7*z+12 = 0

z^2+7*z+12 = 0

DELTA = 7^2-(1*4*12)

DELTA = 1

DELTA > 0

z = (1^(1/2)-7)/(1*2) or z = (-1^(1/2)-7)/(1*2)

z = -3 or z = -4

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

z^2-2*z-3 = 0

z^2-2*z-3 = 0

DELTA = (-2)^2-(-3*1*4)

DELTA = 16

DELTA > 0

z = (16^(1/2)+2)/(1*2) or z = (2-16^(1/2))/(1*2)

z = 3 or z = -1

(z+1)*(z-3) = 0

((z+4)*(z+1)*(z-3))/(z+1) = 0

( z+1 )

z+1 = 0 // - 1

z = -1

( z+4 )

z+4 = 0 // - 4

z = -4

( z-3 )

z-3 = 0 // + 3

z = 3

z in { -1} 

z in { -4, 3 }