How do i solve algebraically for n. 9n=3(nP2)

n. 9n=3(nP2)

=>9n^2=3(n!/(n-2)!)
=>9n^2=3(n*(n-1)(n-2)!/(n-2)!)
=>9n^2=3(n*(n-1))
=>9n^2=3(n^2-n)
=>9n^2=3n^2-3n
=>6n^2-3n=0
=>3n(n-2)=0
=>n=0 and n=2

Did you understand harley?

Yes, i just didn't know how to start with the 9n, thank you!

oops,I made a mistake

6n^2+3n=0
=> 3n(2n+1)=0
=>n= 0 and n= -1/2

The mistake was in starting with 9n and the saying 9n^2.

9n=3(nP2)
=>9n=3(n*(n-1))
=>9n=3n^2-3n
=>3n^2-12n = 0
=> 3n(n-4) = 0
=> n = 0,4

To solve the equation algebraically for n, follow these steps:

Step 1: Understand the equation.
- The equation is 9n = 3(nP2).
- Here, "nP2" represents the permutation of n taken 2 at a time.

Step 2: Expand the expression.
- The expression "nP2" represents n factorial divided by (n-2) factorial.
- So, nP2 can be expanded as n! / (n-2)!.

Step 3: Simplify the expression.
- Simplify nP2 to n! / (n-2)!.
- Simplify the equation: 9n = 3(n! / (n-2)!).

Step 4: Eliminate the fraction by multiplying both sides by (n-2)!.
- Multiply both sides of the equation by (n-2)!.
- The equation becomes 9n * (n-2)! = 3(n!).

Step 5: Simplify the right side of the equation.
- Expand 3(n!) as 3 * n!.
- The equation becomes 9n * (n-2)! = 3 * n!.

Step 6: Divide both sides by n! to isolate n.
- Divide both sides of the equation by n!.
- The equation becomes (9n * (n-2)!)/n! = 3.

Step 7: Simplify the left side of the equation.
- Simplify (n-2)! / n! as 1/n * (n-1).
- The equation becomes 9n * (1/n * (n-1)) = 3.

Step 8: Simplify further.
- Cancel out the n in the numerator and denominator on the left side of the equation.
- The equation becomes 9 * (n-1) = 3.

Step 9: Solve for n.
- Distribute 9 to (n-1) on the left side of the equation.
- The equation becomes 9n - 9 = 3.

Step 10: Isolate the variable by adding 9 to both sides of the equation.
- Add 9 to both sides of the equation.
- The equation becomes 9n = 3 + 9.

Step 11: Simplify further.
- 3 + 9 is equal to 12.
- The equation becomes 9n = 12.

Step 12: Solve for n by dividing both sides by 9.
- Divide both sides of the equation by 9.
- The equation becomes n = 12/9.

Step 13: Simplify the division.
- 12 divided by 9 is equal to 1 and a remainder of 3.
- The equation becomes n = 1 + (3/9).

Step 14: Simplify the fraction.
- 3/9 can be reduced to 1/3.
- The equation becomes n = 1 + 1/3.

Now, n is equal to 1 + 1/3 or 1.33 (rounded to two decimal places).