Not sure I'm doing this the right way

I need to solve this in terms of x

3y(3y-x) = 2z(x+2z)

9y^{2} - 3yx = 2zx + 4z^{2}

9y^{2} - 4z^{2} = 3yx + 2zx

(9y - 4z)(9y + 4z) = x(2z + 3y)

x = (9y - 4z)(9y + 4z) / (2z + 3y)

don't know if I can cancel to give this

x = (3y - 2z)(3y + 2z)

x = 9y^{2} + 3y2z - 3y2z - 4b^{2}

x = 9y^{2} - 4b^{2}

Really don't know if I've done this properly. Can anyone help?

Thanks.

Re: Not sure I'm doing this the right way

Quote:

Originally Posted by

**kx110** I need to solve this in terms of x

3y(3y-x) = 2z(x+2z)

9y^{2} - 3yx = 2zx + 4z^{2}

9y^{2} - 4z^{2} = 3yx + 2zx

(9y - 4z)(9y + 4z) = x(2z + 3y)

x = (9y - 4z)(9y + 4z) / (2z + 3y)

this is as far as you can go ...

Re: Not sure I'm doing this the right way

I thought it might be, I was just guessing with the rest. Do you think it's necessary to convert 9y^{2} - 4z^{2} to (9y - 4z)(9y + 4z) or is that over complicating it?

Thanks for your help.

Re: Not sure I'm doing this the right way

Quote:

Originally Posted by

**kx110** I thought it might be, I was just guessing with the rest. Do you think it's necessary to convert 9y^{2} - 4z^{2} to (9y - 4z)(9y + 4z) or is that over complicating it?

Thanks for your help.

it's a matter of choice ... I prefer to have it factored in case one has to find zeros of the expression, etc.