How to solve this problem? we just now learned this in algebra, and my teacher didn't explain it quite good.

*Before I begin, I am not sure why there are two different variables, they should both be the same. So, I am just going to use n as the variable

Set the equation up so that it equals zero. To do that, add 15 on both sides of the equation

n² + 8n + 15 = 0

Now, to factor, find 2 numbers that multiply to get 15, but also add up to get 8

The 2 numbers that multiply to get 15 are 3 and 5. 3 and 5 also add up to get 8

Now, put 3 and 5 into 2 sets of parenthesis

(n + 3)(n + 5)

Now, you can set each set of parenthesis equal to zero and solve

n + 3 = 0

Subtract 3 on both sides of the equation

n = -3

Set the other set of parenthesis equal to zero

n + 5 = 0

Subtract 5

n = -5

So, n= -3 and n= -5

The answer would be 27 because assuming that each package has 1 bar of soap and 1 tube of toothpaste, after 27 packages they would run out of toothpaste