Answer:
[tex]n=0\quad \mathrm{or}\quad \:n=6[/tex]
Step-by-step explanation:
[tex]\left|-2n+6\right|=6\\\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\-2n+6=-6\quad \mathrm{or}\quad \:-2n+6=6\\-2n+6=-6\quad :\quad n=6\\-2n+6=-6\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\-2n+6-6=-6-6\\\mathrm{Simplify}\\-2n=-12\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2n}{-2}=\frac{-12}{-2}\\[/tex]
[tex]Simplify\\\frac{-2n}{-2}=\frac{-12}{-2}\\\mathrm{Simplify\:}\frac{-2n}{-2}:\quad n\\\frac{-2n}{-2}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{2n}{2}\\\mathrm{Divide\:the\:numbers:}\:\frac{2}{2}=1\\=n[/tex]
[tex]\mathrm{Simplify\:}\frac{-12}{-2}:\quad 6\\\frac{-12}{-2}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{12}{2}\\\mathrm{Divide\:the\:numbers:}\:\frac{12}{2}=6\\=6\\n=6\\-2n+6=6\quad :\quad n=0\\-2n+6=6\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\-2n+6-6=6-6\\Simplify\\-2n=0\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2n}{-2}=\frac{0}{-2}[/tex]
[tex]Simplify\\n=0\\\mathrm{Combine\:Solutions:}\\n=0\quad \mathrm{or}\quad \:n=6[/tex]
