Can anyone solve this problem?

Question

Solve 4x^ to the third power - 12 x^ to the second power = 9x-27

Answer 1

4x^3 - 12x^2 - 9x + 27 = 0
4x^2(x - 3) - 9(x - 3) = 0
(4x^2 - 9)(x - 3) = 0
(2x + 3)(2x - 3)(x - 3) = 0
x = {-3/2, 3/2, 3}

Answer 2

Difference of Squares formula:
(a^2 - b^2) = (a-b)(a+b)

first move everything to the left side of the equation:

(4x^3 - 12x^2) - (9x - 27) = 0

Factor each set of () completely:
4x^3 - 12x^2 = 4x^2 (x-3)
9x - 27 = 9 (x -3)

So, now you have:
4x^2 (x-3) - 9 (x-3) = 0

Now you can factor out the (x-3) from each term:
(x-3)(4x^2 - 9) = 0

Now, using Difference of Squares, you can better factor the second term:
4x^2 - 9 = (2x-3)(2x+3)

So, you now have:
(x-3)(2x-3)(2x+3) = 0

Set each of those terms =0 and solve for x:

x-3 = 0
x = 3

2x-3 = 0
2x = 3
x = 3/2

2x+3 = 0
2x = -3
x = -3/2

Those are your three answers.

Answer 3

4x^3 - 12x^2 = 9x - 27
factor out common terms from each side
(4x^2) * (x - 3) = 9 * (x - 3)
4x^2 = 9
x^2 = 9/4
take the square root of both sides
x = +/- 3/2

Answer 4

4x³ - 12 x² = 9x-27
4x²(x - 3) = 9(x - 3)
4x² = 9(x - 3) : (x - 3)
4x² = 9
x = sqrt(9/4)
x' = 3/2 = 1,5
x"= -3/2 = -1,5
Solution: {x elements of R | x = 1,5 or -1,5}
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Answer 5

4x(x^2-3x+9)=0

Thats as far as I got, it is prime. You do the math.

Answer 6

Yes.

Answer 7

4X - 12X= 9X-17 IT WOULD BE 55 (THAT WAS EASY)

Answer 8

True

Answer 9

x=a sub n over x

Answer 10

Nope too hard. Sry.