How Does This Algebraic Equation Simplify to This Result?

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The discussion centers on simplifying the algebraic equation (k*16*10^(-6))/d^2=(k*16e-6)/(30-d)^2 to derive the result 20(3-d)^2=d^2 with d=2. Participants express confusion over the manipulation process, with one user attempting to clarify the equation but ultimately arriving at a different result. The suggestion includes canceling the k terms, reciprocating both sides, and then expanding to solve for d. The conversation highlights the challenges of algebraic manipulation and the importance of accurate equation transcription. The thread emphasizes the need for careful steps in algebra to avoid errors.
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Homework Statement



Was just wondering how this equation:

(k*16*10^(-6))/d^2=(k*16e-6)/(30-d)^2

gets manipulated to produce this result

20(3-d)^2=d^2

d=2

Homework Equations


The Attempt at a Solution



I've tried manipulating it myself but it ends up with me spiraling off into pages of crap that is obviously wrong.
 
Last edited:
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Are you sure you typed that in right?

Were you trying to say this?:
(k*16*10-6)/d2 = (k*16*10-6)/(30-d)2

If so, then first you would cancel the k expressions at the top, reciprocal both sides, expand and solve for d. However, I get a different result than what you give below.
 

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