What number makes each equation true? n^2 + 6 n + 8 = (n-2) (n+ - 9)?

The equation will simplify to a linear equation in n, which can be solved to find n.

n² +6n +8 = (n -2)(n -9) . . . . . . we assume this is your intent

n² +6n +8 = n² -11n +18 . . . . . . expand the right side

17n = 10 . . . . . . . . . . . . . . . . . . . add 11n -8 -n² to both sides

n = 10/17 . . . . . . . . . . divide by the coefficient of n

The number that makes the equation true is n = 10/17.