Why No Solution Here?

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|x^2+4x|=-12

it has no solution because absolute value (by definition) cannot be negative, and here we have -12

so, |x^2+4x|=-12 statement is false
 
|x^2+4x|=-12

it has no solution because absolute value (by definition) cannot be negative, and here we have -12

so, |x^2+4x|=-12 statement is false

In another words, you are saying this:

|expression| = positive is ok.

|expression| = negative DNE.
 

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