Let's solve the equation step-by-step:
1. Start with the initial equation:
[tex]\[ 6n + 9 = -3n - 21 - 6 \][/tex]
2. Simplify the right-hand side by combining like terms:
[tex]\[ -3n - 21 - 6 = -3n - 27 \][/tex]
3. Now, rewrite the equation after this simplification:
[tex]\[ 6n + 9 = -3n - 27 \][/tex]
4. To get all terms involving [tex]\(n\)[/tex] on one side of the equation, add [tex]\(3n\)[/tex] to both sides of the equation:
[tex]\[ 6n + 3n + 9 = -27 \][/tex]
[tex]\[ 9n + 9 = -27 \][/tex]
5. Next, to isolate the term with [tex]\(n\)[/tex], subtract 9 from both sides of the equation:
[tex]\[ 9n + 9 - 9 = -27 - 9 \][/tex]
[tex]\[ 9n = -36 \][/tex]
6. Finally, solve for [tex]\(n\)[/tex] by dividing both sides by 9:
[tex]\[ n = \frac{-36}{9} \][/tex]
[tex]\[ n = -4 \][/tex]
Thus, the solution to the equation [tex]\(6n + 9 = -3n - 21 - 6\)[/tex] is:
[tex]\[ n = -4 \][/tex]
