the difference between the square of a number and the number is 6. What is the number?

Let the number = x
Then sqaure of the number = x²

Difference between them...
x² - x = 6
x² - x - 6 = 0
x² - 3x + 2x - 6 = 0
x(x - 3) + 2( x - 3) = 0
(x - 3)( x + 2) = 0

x - 3 = 0 then x = 3

x + 2 = 0 then x = -2

Check !!

(3)² - 3 = 9 - 3 = 6

(-2)² - (-2) = 4 + 2 = 6

let x = a number
then, x^2 = the square of a number

x^2 - x = 6

solve the quadratic equation: x^2 - x - 6 = 0

factor: (x - 3)(x + 2) = 0

solve: x = 3 or x = - 2

check:
when x = 3,
(3)^2 - 3 = 6

when x = - 2
(- 2)^2 - (- 2) = 4 + 2 = 6

qed

y= number y²-y=6 y²-y-6=0 (y-3)(y+2)=0 Thus, y= 3, -2 <= answers
Check: (3)²-3=6 or (-2)²-(-2)=6

Thank you guys so much. Im not very good at word problems but with your help, i now understand. Thank you so much!!!!

The difference between the square of a number and the number is 6. What is the number?
n^2 - n - 6 = 0
(n - 3)(n + 2) = 0
Solutions:
n = -2
n = 3
The number is -2 or 3.

x² – x = 6
x² – x – 6 = 0
(x + 2)(x – 3) = 0
x + 2 = 0 or x – 3 = 0
x = –2 or x = 3