Question
$$4x^2+28x+49 = (2x+7)^2$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 4x^2+28x+49 &= (2x+7)^2&& \text{simplify right side} \\[1 em]4x^2+28x+49 &= 4x^2+28x+49&& \text{move all terms to the left hand side } \\[1 em]4x^2+28x+49-4x^2-28x-49 &= 0&& \text{simplify left side} \\[1 em]4x^2+28x+49-4x^2-28x-49 &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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