(x^3+2x^2-21x+18)/(x+6)

Solution for (x^3+2x^2-21x+18)/(x+6) equation:

D( x )

x+6 = 0

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

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

(x^3+2*x^2-(21*x)+18)/(x+6) = 0

(x^3+2*x^2-21*x+18)/(x+6) = 0

x^3+2*x^2-21*x+18 = 0

x^3+2*x^2-21*x+18 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18 }

1

x = 1

x^3+2*x^2-21*x+18 = 0

1

x-1

x^2+3*x-18

x^3+2*x^2-21*x+18

x-1

x^2-x^3

3*x^2-21*x+18

3*x-3*x^2

18-18*x

18*x-18

0

x^2+3*x-18 = 0

DELTA = 3^2-(-18*1*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)-3)/(1*2) or x = (-81^(1/2)-3)/(1*2)

x = 3 or x = -6

x in { -6, 3, 1} 

(x+6)*(x-3)*(x-1) = 0

(x-3)*(x-1) = 0

( x-1 )

x-1 = 0 // + 1

x = 1

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 1, 3 }