Solve for x
x^2(x-3)^2-4(x-3)^2=0

Question

Solve for x
x^2(x-3)^2-4(x-3)^2=0

anonymous · Answer

$$x ^{2}(x-3)^{2}-4(x-3)^{2}=0$$

anonymous · Answer

I have $$x ^{2}(x-3)(x-3)-4(x-3)(x-3)=0$$ but I don't know what to do next

anonymous · Answer

That wasn't really necessary :)
It may not be obvious yet, but try letting $$\large u=(x-3)^2$$
Then
$$\large x^2(x-3)^2-4(x-3)^2=x^2u-4u$$

anonymous · Answer

And you can see that u can simply be factored out like this...
$$\large u(x^2-4)$$

anonymous · Answer

I am really confused by what you just posted

anonymous · Answer

And then revert u back to its original meaning, sort of...
$$\large (x-3)^2(x^2-4)$$
What I did was factor out the entire expression (x-3)^2

anonymous · Answer

You don't have to go through the u-part
but I did it so that it's easier to see that it can be factored out :)

anonymous · Answer

ok but from the step that I was at before do you then do
x^2(x^2-6x-6)-4(x^2-6x-6)=0

anonymous · Answer

:)
First of all
(x-3)^2 = x^2 - 6x + 9
Second, you can certainly do that, but you'll have to factor that out again later, so why bother? :)