Answer:
two (n = 4, and n = -1)
Step-by-step explanation:
Let's solve it as follows:
First, we can divide out the common factor of 3 from each side, to get:
n(2n-8) = 8 -2n
Next, we expand, and move all the terms over to the right hand side (so that we have 0 on the LHS - as this is how we will want to solve the quadratic equation):
2n^2 - 8n - 8 +2n = 0
2n^2 - 6n - 8 = 0.
We also see we can further simplify by dividing out the factor of 2, to get:
n^2 -3n -4. = 0
Next, as this is a quadratic, the usual next step is to factorise, to get:
(n-4)(n+1) = 0
So we see that n = 4 and n = -1 are the two solutions.
