`1.`
`a.`
`3x-2=2x-3`
`⇔3x-2x=-3+2`
`⇔x=-1
`b.`
5-(x-6)=4(3-2x)
`⇔5-x+6=12-8x`
`⇔-x+8x=12-5-6`
`⇔7x=1`
`⇔x=(1)/(7)`
`c.`
`(x+1)(2x-3)=(2x-1)(x+5)`
`⇔2x^2-3x+2x-3=2x^2+10x-x-5`
`⇔2x^2-3x+2x-3-2x^2-10x+x+5=0`
`⇔-10x+2=0`
`⇔-10x=-2`
`⇔x=1/5`
`d.`
`(x-3)(x+4)-2(3x-2)=(x-4)^2`
`⇔x^2+4x-3x-12-6x+4=x^2-8x+16`
`⇔x^2+4x-3x-12-6x+4-x^2+8x-16`
`⇔3x-24=0`
`⇔3x=24`
`⇔x=8`
`2.`
`a.`
`x^2-9-(2x-1)(x-3)=0`
`⇔(x+3)(x-3)-(2x-1)(x-3)=0`
`⇔(x-3)(x+3-2x+1)=0`
`⇔(x-3)(4-x)=0`
⇔$\left[\begin{matrix} x-3=0\\ 4-x=0\end{matrix}\right.$
⇔$\left[\begin{matrix} x=3\\ x=4\end{matrix}\right.$
`b.`
`4-x^2+(2+x)(5-3x)=0`
`⇔(2-x)(2+x)+(2+x)(5-3x)=0`
`⇔(2+x)(2-x+5-3x)=0`
`⇔(2+x)(7-4x)=0`
⇔$\left[\begin{matrix} x+2=0\\ 7-4x=0\end{matrix}\right.$
⇔$\left[\begin{matrix} x=-2\\ \dfrac{7}{4}\end{matrix}\right.$
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