Complete the square:
-7x^2+14x-21=0 move constant to other side, add 21 to both sides
-7x^2+14x=21 make the coefficient of x^2=1, divide both sides by -7
x^2-2x=-3 halve the linear coefficient, square it, add it to both sides, +1
x^2-2x+1=-2 now the left side is a perfect square
(x-1)^2=-2 take the square root of both sides
x-1=±√-2 add 1 to both sides
x=1±√-2 note that there are not real roots here because there is no real square root of a negative number...
x=1+i√2 and 1-i√2 so
(x+1+i√2)(x+1-i√2)
