Answer:
n = 2, -4
Explanation:
Given:
[tex]6n^2+12n-45=3[/tex]
Add 45 to both sides:
[tex]\begin{gathered} 6n^2+12n=3+45 \\ \\ 6n^2+12n=48 \end{gathered}[/tex]
Divide both sides by 6
[tex]n^2+2n=8[/tex]
Note that:
[tex](n+1)^2=n^2+2n+1[/tex]
We can simple use this and subtract 1 from the expression as the extra value
[tex](n+1)^2-1=8[/tex]
Add 1 to both sides
[tex](n+1)^2=9[/tex]
Take square roots of both sides
[tex]\begin{gathered} n+1=\pm\sqrt{9} \\ \\ n+1=\pm3 \end{gathered}[/tex]
Therefore;
[tex]\begin{gathered} n+1=3 \\ \\ \Rightarrow n=3-1=2 \end{gathered}[/tex]
and
[tex]\begin{gathered} n+1=-3 \\ \\ \Rightarrow n=-3-1=-4 \end{gathered}[/tex]
