Question
$$15x\cdot2+30x-45 = 15x\cdot2+30x-45$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 15x\cdot2+30x-45 &= 15x\cdot2+30x-45&& \text{simplify left and right hand side} \\[1 em]30x+30x-45 &= 30x+30x-45&& \\[1 em]60x-45 &= 60x-45&& \text{move the $ \color{blue}{ 60x } $ to the left side and $ \color{blue}{ -45 }$ to the right} \\[1 em]60x-60x &= -45+45&& \text{simplify left and right hand side} \\[1 em]60x-60x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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