Question
$$-3(5x+9)+7 = -5\cdot(5+3x)+5$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} -3(5x+9)+7 &= -5\cdot(5+3x)+5&& \text{simplify left and right hand side} \\[1 em]-(15x+27)+7 &= -(25+15x)+5&& \\[1 em]-15x-27+7 &= -25-15x+5&& \\[1 em]-15x-20 &= -15x-20&& \text{move the $ \color{blue}{ -15x } $ to the left side and $ \color{blue}{ -20 }$ to the right} \\[1 em]-15x+15x &= -20+20&& \text{simplify left and right hand side} \\[1 em]-15x+15x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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