$$ \begin{aligned} (2x+1)^4 &= 16x^4+32x^3+24x^2+4x-3&& \text{simplify left side} \\[1 em]16x^4+32x^3+24x^2+8x+1 &= 16x^4+32x^3+24x^2+4x-3&& \text{move all terms to the left hand side } \\[1 em]16x^4+32x^3+24x^2+8x+1-16x^4-32x^3-24x^2-4x+3 &= 0&& \text{simplify left side} \\[1 em]16x^4+32x^3+24x^2+8x+1-16x^4-32x^3-24x^2-4x+3 &= 0&& \\[1 em]4x+4 &= 0&& \text{ move the constants to the right } \\[1 em]4x &= -4&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{4}{4}&& \\[1 em]x &= -1&& \\[1 em] \end{aligned} $$

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