Question
$$-3-2q = -2q+12-15$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} -3-2q &= -2q+12-15&& \text{simplify left and right hand side} \\[1 em]-2q-3 &= -2q-3&& \text{move the $ \color{blue}{ -2q } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]-2q+2q &= -3+3&& \text{simplify left and right hand side} \\[1 em]-2q+2q &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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