[tex]\displaystyle\bf\\(x+4)^{2}-x^{2} =0\\\\(x+4-x)\cdot(x+4+x)=0\\\\4\cdot(2x+4)=0\\\\2x+4=0\\\\2x=-4\\\\\boxed{x=-2}[/tex]
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[tex]\displaystyle\bf\\(x+4)^{2}-x^{2} =0\\\\(x+4-x)\cdot(x+4+x)=0\\\\4\cdot(2x+4)=0\\\\2x+4=0\\\\2x=-4\\\\\boxed{x=-2}[/tex]