factor:

2x^2(x-3)+12x(3-x)-18(x-3)

2x^2(x-3)+12x(3-x)-18(x-3)

2x^2(x-3)-12x(x-3)-18(x-3)
(x-3)(2x^2-12x-18)
2(x-3)(x^2-6x-9)
2(x-3)(...wondering if you had a typo on the -18. If it was +18, it would have been simple..
2(x-3)^3
as it is,

x=3+-sqrt(18)
2(x-3)(x-3-3sqrt2)(x-3+3sqrt2)

To factor the given expression:

2x^2(x-3) + 12x(3-x) - 18(x-3)

We can break it down step by step using the distributive property and combining like terms:

Step 1: Distribute the coefficients 2x^2 and -18 to (x-3) and distribute 12x to (3-x).

2x^2(x) - 2x^2(3) + 12x(3) - 12x(x) - 18(x) + 18(3)

Simplifying further:

2x^3 - 6x^2 + 36x - 12x^2 - 18x + 54

Step 2: Combine like terms:

(2x^3) + (-6x^2 - 12x^2) + (36x - 18x) + 54

Simplifying further:

2x^3 - 18x^2 + 18x + 54

So, the fully factored expression is:

2x^3 - 18x^2 + 18x + 54