What is X? 27=x^2-6x

Beginning with 27=x^2-6x, subtract 27 from both sides to have a second order polynomial equation equal to zero:

x ² - 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