Question
$$(2x+1)^2 = (3x-5)^2$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 4 }{ 5 } & x_2 = 6 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (2x+1)^2 &= (3x-5)^2&& \text{simplify left and right hand side} \\[1 em]4x^2+4x+1 &= 9x^2-30x+25&& \text{move all terms to the left hand side } \\[1 em]4x^2+4x+1-9x^2+30x-25 &= 0&& \text{simplify left side} \\[1 em]-5x^2+34x-24 &= 0&& \\[1 em] \end{aligned} $$
$ -5x^{2}+34x-24 = 0 $ is a quadratic equation.
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