$\text{a)}$  

$3{\left(x+1\right)}^2-2\left(x-1\right)=3\left(x-1\right)\left(x+1\right)$  

$3\left(x^2+2x+1\right)-2x+2=3\left(x^2-1\right)$  

$3x^2+6x+3-2x+2=3x^2-3\mid -3x^2$       

$4x+5=-3\mid -5$  

$4x=-8\mid :4$  

$x=-2$  

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$\text{b)}$  

$5x-2\left(x+4\right)+4x^2={\left(2x-3\right)}^2-4\left(2-x\right)+2$  

$5x-2x-8+4x^2=4x^2-12x+9-8+4x+2\mid -4x^2$  

$3x-8=-8x+3\mid +8x+8$  

$11x=11\mid :11$  

$x=1$  

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$\text{c)}$  

$\frac{x+2}{2}-5\cdot \frac{3-x}{3}=\frac{2x-2}{6}\mid \cdot 6$  

$3\left(x+2\right)-5\cdot 2\cdot \left(3-x\right)=2x-2$  

$3x+6-30+10x=2x-2$  

$13x-24=2x-2\mid -2x+24$  

$11x=22\mid :11$  

$x=2$  

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$\text{d)}$  

$2\frac{1}{4}\cdot \left(\frac{16}{27}x-1\frac{1}{3}\right)-\frac{3-4x}{4}=\frac{3-2x}{2}+1$  

$\frac{9}{4}\cdot \left(\frac{16}{27}x-\frac{4}{3}\right)-\frac{3-4x}{4}=\frac{3-2x}{2}+1\mid \cdot 4$  

$9\left(\frac{16}{27}x-\frac{4}{3}\right)-\left(3-4x\right)=2\cdot \left(3-2x\right)+4$  

$\frac{16}{3}x-12-3+4x=6-4x+4$  

$5\frac{1}{3}x-15+4x=10-4x$  

$9\frac{1}{3}x-15=10-4x\mid +4x+15$  

$13\frac{1}{3}x=25$  

$\frac{40}{3}x=25\mid :\frac{40}{3}$  

$x=25\cdot \frac{3}{40}$  

$x=\frac{75}{40}$  

$x=\frac{15}{8}$  

$x=1\frac{7}{8}$