solve for x: (3x+1)(x+2)=-1

(3x+1)(x+2)=-1

(3x+1)(x+2)=-1

(3x)(x) (3x)(2) (1)(x) (1)(2)=-1

3x^2 +6x +x +2=-1

3x^2 +7x+2=-1

3x^2+7x+2=-1

3x^2+7x+2/3=-1/3

x^2+7x/3+2/3=-1/3

x^2+7x/3+2/3-2/3=-1/3-2/3

x^2+7x/3=-1

x^2+7x/3+49/36=-1+49/36 (1/2 coef of x then squared)

x^2+7x/3+49/36=13/36

(x+7/6)^2=13/36 (remove exponent by sq rt of both sides)

x+7/6=+/- sqr rt 13/6

Solve:

x+7/6=sq rt 13/6

x=(sq rt13/6)-7/6

and

x-7/6=sq rt 13/6

x=(sq rt13/6)+7/6