$$(2x+1)^2-3(2x-1)(2x+1) = -2(2x+1)(2x-3)$$

$$ \begin{aligned} (2x+1)^2-3(2x-1)(2x+1) &= -2(2x+1)(2x-3)&& \text{simplify left and right hand side} \\[1 em]4x^2+4x+1-3(2x-1)(2x+1) &= -(4x+2)(2x-3)&& \\[1 em]4x^2+4x+1-(6x-3)(2x+1) &= -(8x^2-12x+4x-6)&& \\[1 em]4x^2+4x+1-(12x^2+6x-6x-3) &= -(8x^2-8x-6)&& \\[1 em]4x^2+4x+1-(12x^2-3) &= -8x^2+8x+6&& \\[1 em]4x^2+4x+1-12x^2+3 &= -8x^2+8x+6&& \\[1 em]-8x^2+4x+4 &= -8x^2+8x+6&& \text{move all terms to the left hand side } \\[1 em]-8x^2+4x+4+8x^2-8x-6 &= 0&& \text{simplify left side} \\[1 em]-8x^2+4x+4+8x^2-8x-6 &= 0&& \\[1 em]-4x-2 &= 0&& \text{ move the constants to the right } \\[1 em]-4x &= 2&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= -\frac{2}{4}&& \\[1 em]x &= -\frac{1}{2}&& \\[1 em] \end{aligned} $$

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