Question
$$4(2x+3) = x\cdot(3+5)+12$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 4(2x+3) &= x\cdot(3+5)+12&& \text{simplify left and right hand side} \\[1 em]8x+12 &= x\cdot8+12&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]8x-8x &= 12-12&& \text{simplify left and right hand side} \\[1 em]8x-8x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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