Question
$$4(4x+3)^2-11 = 25$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -\dfrac{ 3 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4(4x+3)^2-11 &= 25&& \text{simplify left side} \\[1 em]4(16x^2+24x+9)-11 &= 25&& \\[1 em]64x^2+96x+36-11 &= 25&& \\[1 em]64x^2+96x+25 &= 25&& \text{move all terms to the left hand side } \\[1 em]64x^2+96x+25-25 &= 0&& \text{simplify left side} \\[1 em]64x^2+96x+25-25 &= 0&& \\[1 em]64x^2+96x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 64x^{2}+96x = 0 } $, first we need to factor our $ x $.
$$ 64x^{2}+96x = x \left( 64x+96 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ 64x+96 = 0$.
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