can someone please help explain how to do this problem. i have a previous posting where i tried to work the problem out, and someone tried to explain where i was confused, but im still confused.

4(2n+1)=3(6n+3)+1

Sure, I can help you with the problem. Let's go through it step by step.

The given equation is: 4(2n+1) = 3(6n+3) + 1

Step 1: Distribute the multiplication on both sides of the equation.
On the left side, we have 4 multiplied by (2n+1), which means we multiply 4 by 2n and 4 by 1 separately:
8n + 4

On the right side, we have 3 multiplied by (6n+3), which means we multiply 3 by 6n and 3 by 3 separately:
18n + 9

Now we can rewrite the equation as:
8n + 4 = 18n + 9 + 1

Step 2: Combine like terms.
On the right side, we add the constants 9 and 1 to get 10:
8n + 4 = 18n + 10

Step 3: Move the variables to one side and the constants to the other side of the equation.
To do this, we subtract 8n from both sides to isolate the variables on the left side:
8n - 8n + 4 = 18n - 8n + 10

Simplifying further, we have:
4 = 10n + 10

Next, we subtract 10 from both sides to isolate the variables on the right side:
4 - 10 = 10n + 10 - 10

Simplifying further, we have:
-6 = 10n

Step 4: Solve for n by dividing both sides by 10.
To find the value of n, we divide both sides of the equation by 10:
-6/10 = 10n/10

Simplifying further, we have:
-0.6 = n

Therefore, the solution to the equation is n = -0.6.

I hope this explanation helps you understand the steps involved in solving this problem. Let me know if you have any further questions!