`7, 3x(x + 5) - 2x - 10 = 0`
`⇔ 3x(x + 5) - 2(x + 5) = 0`
`⇔ (3x - 2)(x + 5) = 0`
`⇔` \(\left[ \begin{array}{l}3x-2=0\\x+5=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{2}{3}\\x=-5\end{array} \right.\)
`8, x - 3 + 3x(x - 3) = 0`
`⇔ (x - 3)(3x + 1) = 0`
`⇔` \(\left[ \begin{array}{l}x-3=0\\3x+1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=3\\x=\dfrac{-1}{3}\end{array} \right.\)
`9, 3x - 2 + 2x(3x - 2) = 0`
`⇔ (3x - 2)(2x + 1) = 0`
`⇔` \(\left[ \begin{array}{l}3x-2=0\\x+5=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{2}{3}\\x=-5\end{array} \right.\)
`11, 2x - 4 + 3x(x - 2) = 0`
`⇔ 2(x - 2) + 3x(x - 2) = 0`
`⇔ (3x + 2)(x - 2) = 0`
`⇔` \(\left[ \begin{array}{l}3x+2=0\\x-2=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-2}{3}\\x=2\end{array} \right.\)
`12, x(x + 2) + 2 = -x`
`⇔ x^2 + 2x + 2 + x = 0`
`⇔ x(x + 1) + 2(x + 1) = 0`
`⇔ (x + 2)(x + 1) = 0`
`⇔` \(\left[ \begin{array}{l}x+2=0\\x+1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=-2\\x=-1\end{array} \right.\)
`14, 3x(x - 3) = -x + 3`
`⇔ 3x(x - 3) = -(x - 3)`
`⇔ 3x(x - 3) + (x - 3) = 0`
`⇔ (3x + 1)(x - 3) = 0`
`⇔` \(\left[ \begin{array}{l}x+2=0\\x+1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-1}{3}\\x=3\end{array} \right.\)
`15, 4(x - 5) = 5 - x`
`⇔ 4(x - 5) = -(x - 5)`
`⇔ 4(x - 5) + (x - 5) = 0`
`⇔ (x - 5)(4 + 1) = 0`
`⇔ 5(x - 5) = 0`
`⇔ x - 5 = 0`
`⇔ x = 5`
`16, x^2 - 3x = 4(x - 3)`
`⇔ x(x - 3) - 4(x - 3) = 0`
`⇔ (x - 4)(x - 3) = 0`
`⇔` \(\left[ \begin{array}{l}x-4=0\\x-3=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=4\\x=3\end{array} \right.\)
`17, x^2 -x - (3x - 3) = 0`
`⇔ x(x - 1) - 3(x - 1) = 0`
`⇔ (x - 1)(x - 3) = 0`
`⇔` \(\left[ \begin{array}{l}x-1=0\\x-3=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=1\\x=3\end{array} \right.\)
`18, (x - 3)2 = -x + 3`
`⇔ 2(x - 3) = -(x - 3)`
`⇔ 2(x - 3) + (x - 3) = 0`
`⇔ (x - 3)(2 + 1) = 0`
`⇔ 3(x - 3) = 0`
`⇔ x - 3 = 0`
`⇔ x = 3`
`19, (x - 2)2 - x + 2 = 0`
`⇔ 2(x - 2) - (x - 2) = 0`
`⇔ (x - 2)(2 - 1) = 0`
`⇔ x - 2 = 0`
`⇔ x = 2`
`20, (2x - 3)2 = 2x - 3`
`⇔ 2(2x - 3) - (2x - 3) = 0`
`⇔ (2 - 1)(2x - 3) = 0`
`⇔ 2x - 3 = 0`
`⇔ 2x = 3`
`⇔ x = 3/2`
`21, (2x - 1)2 + (2 - x)(2x - 1) = 0`
`⇔ (2x - 1)(2 + 2 - x) = 0`
`⇔ (2x - 1)(4 - x) = 0`
`⇔` \(\left[ \begin{array}{l}2x-1=0\\4-x=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=4\end{array} \right.\)
`22, (3x + 4)(x - 4) = (x - 4)2`
`⇔ (3x + 4)(x - 4) - 2(x - 4) = 0`
`⇔ (3x + 4 - 2)(x - 4) = 0`
`⇔ (3x + 2)(x - 4) = 0`
`⇔` \(\left[ \begin{array}{l}3x+2=0\\x-4=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-2}{3}\\x=4\end{array} \right.\)
