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.

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