`a)x²+4x=0`
`⇔x(x+4)=0`
`⇔`$\left[\begin{matrix} x=0\\ x+4=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=0\\ x=-4\end{matrix}\right.$
Vậy `x∈{0;-4}`
`b)5x.(3x-2)=4-9x²`
`⇔5x(3x-2)=-(9x²-4)`
`⇔5x(3x-2)=-(3x+2)(3x-2)`
`⇔5x(3x-2)+(3x+2)(3x-2)=0`
`⇔(3x-2)(5x+3x+2)=0`
`⇔(3x-2)(8x+2)=0`
`⇔`$\left[\begin{matrix} 3x-2=0\\ 8x+2=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} 3x=2\\ 8x=-2\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=\dfrac{2}{3}\\ x=-\dfrac{1}{4}\end{matrix}\right.$
Vậy `x∈{2/3;-1/4}`
`c)2x²+5x=12`
`⇔2x²+5x-12=0`
`⇔2x²+8x-3x-12=0`
`⇔2x(x+4)-3(x+4)=0`
`⇔(x+4)(2x-3)=0`
`⇔`$\left[\begin{matrix} x+4=0\\ 2x-3=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=-4\\ x=\dfrac{3}{2}\end{matrix}\right.$
Vậy `x∈{-4;3/2}`
`d)(x-1/3)^2-(x-1/3)(2x+1)=0`
`⇔(x-1/3)[(x-1/3)-(2x+1)]=0`
`⇔(x-1/3)(x-1/3-2x-1)=0`
`⇔(x-1/3)(-x-4/3)=0`
`⇔`$\left[\begin{matrix} x-\dfrac{1}{3}=0\\ -x-\dfrac{4}{3}=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=\dfrac{1}{3}\\ x=-\dfrac{4}{3}\end{matrix}\right.$
Vậy `x∈{1/3;-4/3}`
`e)2x²-5x=0`
`⇔x(2x-5)=0`
`⇔`$\left[\begin{matrix} x=0\\ 2x-5=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=0\\ x=\dfrac{5}{2}\end{matrix}\right.$
Vậy `x∈{0;5/2}`
`f)(x+3)²-(x+2)(x-2)=4x+17`
`⇔x²+6x+9-(x²-4)=4x+17`
`⇔x²+6x+9-x²+4=4x+17`
`⇔(x²-x²)+6x+(9+4)=4x+17`
`⇔6x+13=4x+17`
`⇔6x-4x=17-13`
`⇔2x=4`
`⇔x=4:2`
`⇔x=2`
Vậy `x=2`
`g)3x²+7x=10`
`⇔3x²+7x-10=0`
`⇔3x²-3x+10x-10=0`
`⇔3x(x-1)+10(x-1)=0`
`⇔(x-1)(3x+10)=0`
`⇔`$\left[\begin{matrix} x-1=0\\ 3x+10=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=1\\ x=-\dfrac{10}{3}\end{matrix}\right.$
Vậy `x∈{1;-10/3}`
`h)(x-3)(x²+3x+9)-x(x²-4)=1`
`⇔x³-27-x³+4x=1`
`⇔4x-27=1`
`⇔4x=1+27`
`⇔4x=28`
`⇔x=28:4`
`⇔x=7`
Vậy `x=7`
