Algebra 2 Question... plz help!?

Question

How do I find all values of u satisfying the equation

- (2u) / (u - 6) = - (18) / (u^2 - 6u)

(If there is more than one solution, separate them with commas.)

Answer 1

cross multiply
-(2u)(u^2-6u)=-(18)(u-6)
negatives cancel
you can extract (u-6) from the left side
(2u)(u-6)(u)=(18)(u-6)
then left with
(2u)(u)=18
u^2=9
u=-3 and u=3

Answer 2

-2u/(u -6) = -18/u^2 - 6u
Cross multiplication
(-2u) (u^2 - 6u) = (-18)(u - 6)
-2u^3 + 12u^2 = -18u + 108
-2u^3 + 12u^2 + 18u - 108 = -18u + 18u + 108 -108
-2u^3 + 12u^2 + 18u - 108 = 0
-2(u^3 - 6u^2 - 9u + 54) = 0
Divide the equation by -2
u^3 - 6u^2 -9u + 54 = 0
Grouping the first and second term, third and fourth term
(u^3 - 6u^2) - (9u - 54) = 0
Factor the groupings
u^2(u - 6) - 9(u - 6) = 0
(u^2 - 9)(u - 6) = 0
To make this equation true,
u^2 - 9 = 0 or u - 6 = 0
If u^2 - 9 = 0
u^2 = 9
u = 3 and - 3
If u - 6 = 0
u = 6
Therefore
u = 3, -3, 6

Answer 3

1. multiply both sides by (u-6)
so: -(2u) = -18(u-6)/(u^2-6u)

2. multiply both sides by (u^2-6u)
so: -(2u)(u^2-6u) = -18(u-6)

3. expand everything
so: -2u^3+12u^2=-18u+108

4. move everything over to one side
so: 2u^3-12u^2-18u+108=0

5. simplify further
so: u^3-6u^2-9u+54=0

5. now you can solve for zeros, however you've been taught. i would just plug the equation into the graphing calculator, graph it and find wherever the line meets the x-axis. if you have to show your work you can do this:
u^3-6u^2-9u+54=u^2(u-6)-9(u-6)
=(u^2-9)(u-6) = 0
you should have been taught this method... anyhoo so by this equation, (u^2-9)(u-6) = 0, we know that either u^2-9=0, or u-6=0
solve for u in both equations and you will get

u=3, -3, and 6

--> you can check this answer by plugging the equation into ur graphing calculator, Y1=u^3-6u^2-9u+54, and you will see that u=3, -3, and 6
:-D

Answer 4

u^2 -6u = (u)(u-6) so

-2u = -18 / u
so

2u^2 = 18
so u = +3,-3

Answer 5

- (2u) / (u - 6) = - (18) / (u^2 - 6u)
- (2u) / (u - 6) + (18) / (u^2 - 6u) = 0
[-(2u)(u) + (18)]/(u^2 - 6u) = 0
[-(2u)(u) + (18)] = 0
-2u^2 + 18 = 0
2u^2 = 18
u^2 = 9
u = -3,+3

Answer 6

2u / (u - 6) = 18 / (u.(u - 6))
2u² = 18
u² = 9
u = ± 3
u = - 3, u = 3