Question

(2x-6)²=3(x-4) factorise
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Answer 1

Putting formula (x-y)^2 = x^2 -2xy+y^2
4x^2 - 24x + 36 = 3x-4x
4x^2 - 24x +36 - 3x -4x
4x^2 - 17x + 36= 0

Answer 2

< (a-b)^2=a^2+b^2-2ab >
So,
(2x -6)^2=3(x-4)
(2x)^2 +6^2- 2.(2x).6= 3x-12

Solve LHS and bring RHS to LHS for easier solving and calculations:

4x^2 + 36 - 24x - 3x + 12 =0
4x^2 -27x + 48 =0

Now use middle term splitting
to factorise and your answer will come out