Question 684653
x^2+12x+27=0


(x+9)(x+3) = 0 ... Note: 9 and 3 both add to 12 and multiply to 27 at the same time


x+9=0 or x+3=0 


x=-9 or x = -3


So the solutions are x=-9 or x = -3


========================================================================================


x^2+6x–7=0


(x+7)(x-1) = 0 ... Note: 7 and -1 both add to 6 and multiply to -7 at the same time


x+7 = 0 or x-1 = 0 


x = -7 or x = 1


So the solutions are x = -7 or x = 1

========================================================================================

12m^2+24m+12=0 


12(m^2+2m+1)=0 


12(m+1)(m+1)=0  ... Note: 1 and 1 both add to 2 and multiply to 1 at the same time


(m+1)(m+1)=0


m+1 = 0 or m+1 = 0 


m = -1 or m = -1


So the only solution is m = -1