$$ \begin{aligned} 9x(4x-3) &= (2x+3)^3-8x(x-1)(x+1)&& \text{simplify left and right hand side} \\[1 em]36x^2-27x &= 8x^3+36x^2+54x+27-8x(x-1)(x+1)&& \\[1 em]36x^2-27x &= 8x^3+36x^2+54x+27-(8x^2-8x)(x+1)&& \\[1 em]36x^2-27x &= 8x^3+36x^2+54x+27-(8x^3+8x^2-8x^2-8x)&& \\[1 em]36x^2-27x &= 8x^3+36x^2+54x+27-(8x^3-8x)&& \\[1 em]36x^2-27x &= 8x^3+36x^2+54x+27-8x^3+8x&& \\[1 em]36x^2-27x &= 8x^3+36x^2+54x+27-8x^3+8x&& \\[1 em]36x^2-27x &= 36x^2+62x+27&& \text{move all terms to the left hand side } \\[1 em]36x^2-27x-36x^2-62x-27 &= 0&& \text{simplify left side} \\[1 em]36x^2-27x-36x^2-62x-27 &= 0&& \\[1 em]-89x-27 &= 0&& \text{ move the constants to the right } \\[1 em]-89x &= 27&& \text{ divide both sides by $ -89 $ } \\[1 em]x &= -\frac{27}{89}&& \\[1 em] \end{aligned} $$

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