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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
yes, |x^2+4x|=12 have solutions -6, and 2
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In another words, you are saying this:
|expression| = positive is ok.
|expression| = negative DNE.
And |expression|= 0 is ok.