How many Solutions are in the equation 3n (2n-8) = 24-6n

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.