Question
$$-6(x+1) = -2(3x+3)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} -6(x+1) &= -2(3x+3)&& \text{simplify left and right hand side} \\[1 em]-(6x+6) &= -(6x+6)&& \\[1 em]-6x-6 &= -6x-6&& \text{move the $ \color{blue}{ -6x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]-6x+6x &= -6+6&& \text{simplify left and right hand side} \\[1 em]-6x+6x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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