Beginning with 27=x^2-6x, subtract 27 from both sides to have a second order polynomial equation equal to zero:
x² - 6x - 27 = 0
Since you can factor the constant term -27 several ways, find the one whose factors can sum to -6.
-9*3 = -27 and 9*-3 = -27
-9 + 3 = -6 so we know these are the factors we want
Now 0 = (x-9)*(x+3)
Since any number multiplied by zero is zero, we need values of x that will make this equation true.
If x = 9, 0 = (9-9)*(9+3) = 0*12 = 0
If x = -3, 0 = (-3-9)*(-3+3) = -12*0 = 0
x = -3, 9
