Question
$$9(14d+9)+4d = 13(10d+6)+3$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 9(14d+9)+4d &= 13(10d+6)+3&& \text{simplify left and right hand side} \\[1 em]126d+81+4d &= 130d+78+3&& \\[1 em]130d+81 &= 130d+81&& \text{move the $ \color{blue}{ 130d } $ to the left side and $ \color{blue}{ 81 }$ to the right} \\[1 em]130d-130d &= 81-81&& \text{simplify left and right hand side} \\[1 em]130d-130d &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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