Question
$$2n+6 = 2\cdot(3+n)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 2n+6 &= 2\cdot(3+n)&& \text{simplify right side} \\[1 em]2n+6 &= 6+2n&& \\[1 em]2n+6 &= 2n+6&& \text{move the $ \color{blue}{ 2n } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]2n-2n &= 6-6&& \text{simplify left and right hand side} \\[1 em]2n-2n &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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