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Math Help - Rearranging an equation

  1. #1
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    Rearranging an equation

    I have the following equation:
    t(t - x) = 3y(3y - x)

    And I need to rearrange it to find x in the terms of y and t, in simplest form. (Assuming that 3y - t is not equal to 0).

    Please could anyone be so kind as to show me how to get to the answer and more importantly, the workings...

    I would also be highly appreciative if someone could point me to some online examples...

    Thanks in advance, Mez
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by mezhopking View Post
    I have the following equation:
    t(t - x) = 3y(3y - x)

    And I need to rearrange it to find x in the terms of y and t, in simplest form. (Assuming that 3y - t is not equal to 0).

    Please could anyone be so kind as to show me how to get to the answer and more importantly, the workings...

    I would also be highly appreciative if someone could point me to some online examples...

    Thanks in advance, Mez
    t(t-x)=3y(3y-x)

    Distribute...

    t^2-tx=9y^2-3xy

    Get terms with x on left side, and terms without x on the right side...

    3xy-tx=9y^2-t^2

    Factor out the x on the left side...

    x(3y-t)=9y^2-t^2

    Divide both sides by (3y-t)

    x=\frac{9y^2-t^2}{3y-t}

    Factor numerator (difference of squares)

    x=\frac{(3y-t)(3y+t)}{(3y-t)}

    \boxed{x=3y+t}

    Google "Literal Equations" to find more examples and tutorials.
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  3. #3
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    Thank you so much!
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