The square of a number is 12 less than 7 times the number. what is the number

First lets write out the equation
7x - 12 = x^2
7x = x^2 + 12
x^2 - 7x + 12
then factor
(x-4)(x-3)
x= 4, 3
To check if we have any extraneous solutions we plug them back into our equation.
(4)^2 - 7(4) + 12 = 0
(3)^2 - 7(3) + 12 = 0

since they both equal 0, your answer is both 4 and 3