Please factorise x/x-4 = x-3?

x/(x-4) = x-3
x = (x-4)*(x-3)
x = x^2 -7x +12
x^2 -7x -x +12 = 0
x^2-8x+12 =0
(x -6)(x-2) = 0
x =6 or x = 2

Question is incorrect.
SHOULD read as :-
x / (x - 4) = x - 3
x = (x - 3)(x - 4)
x = x² - 7x + 12
x² - 8x + 12 = 0
(x - 6)(x - 2) = 0
x = 6 , x = 2

x/(x - 4) = x - 3
x = (x - 4)(x - 3)
x = x*x - 4*x - x*3 + 4*3
x = x^2 - 4x - 3x + 12
x^2 - 7x - x + 12 = 0
x^2 - 8x + 12 = 0
x^2 - 2x - 6x + 12 = 0
(x^2 - 2x) - (6x - 12) = 0
x(x - 2) - 6(x - 2) = 0
(x - 2)(x - 6) = 0

x - 2 = 0
x = 2

x - 6 = 0
x = 6

∴ x = 2 , 6

x = (x-3)*(x-4)
x = x^2 - 4x - 3x +12
x = x^2 -7x +12
0 = x^2 -8x +12
0 = (x - 6)*(x - 2)

x = 6 and x = 2

from the equation
x=x^2-7x +12
or x^2-8x+ !2
or (x-6)(x-2) [breaking -8x= -6x -2x and then taking common]
x=6 or 2

x / (x - 4) = x - 3

Cross multiply:

(x - 4)(x - 3) = x

Expand (using FOIL or whatever method):

x² - 3x - 4x + 12 = x
x² - 3x - 4x + 12 - x = 0

Collect like terms:

x² - 8x + 12 = 0

Factorise:

(x - 6)(x - 2) = 0

x = 6 and 2