1: \(\left(2x+3\right)^2=\left(x-5\right)^2\)
=>\(\left(2x+3\right)^2-\left(x-5\right)^2=0\)
=>\(\left(2x+3+x-5\right)\left(2x+3-x+5\right)=0\)
=>(3x-2)(x+8)=0
=>\(\left[{}\begin{matrix}3x-2=0\\x+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-8\end{matrix}\right.\)
2: \(4x^2-1=\left(2x+1\right)\left(3x-5\right)\)
=>\(\left(2x+1\right)\left(3x-5\right)=\left(2x+1\right)\left(2x-1\right)\)
=>\(\left(2x+1\right)\left(3x-5-2x+1\right)=0\)
=>(2x+1)(x-4)=0
=>\(\left[{}\begin{matrix}2x+1=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=4\end{matrix}\right.\)
3: \(\left(x-3\right)^2-9+x^2=\left(x-3\right)\left(x+1\right)\)
=>\(\left(x-3\right)^2+\left(x-3\right)\left(x+3\right)-\left(x-3\right)\left(x+1\right)=0\)
=>\(\left(x-3\right)\left(x-3+x+3-x-1\right)=0\)
=>(x-3)(x-1)=0
=>\(\left[{}\begin{matrix}x-3=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
4: \(\left(2x+5\right)^2-25+4x^2=\left(2x+5\right)\left(5-9x\right)\)
=>\(\left(2x+5\right)^2+\left(2x-5\right)\left(2x+5\right)=\left(2x+5\right)\left(5-9x\right)\)
=>\(\left(2x+5\right)\left(2x+5+2x-5-5+9x\right)=0\)
=>(2x+5)(13x-5)=0
=>\(\left[{}\begin{matrix}2x+5=0\\13x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{5}{2}\\x=\dfrac{5}{13}\end{matrix}\right.\)
5: 3x(x-5)+6(x-5)=0
=>(x-5)(3x+6)=0
=>\(\left[{}\begin{matrix}x-5=0\\3x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)
6: \(2x\left(x+7\right)+9\left(x+7\right)=0\)
=>(x+7)(2x+9)=0
=>\(\left[{}\begin{matrix}x+7=0\\2x+9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-7\\x=-\dfrac{9}{2}\end{matrix}\right.\)
7: x(2x-1)+5(2x-1)=0
=>(2x-1)(x+5)=0
=>\(\left[{}\begin{matrix}2x-1=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-5\end{matrix}\right.\)
8: \(\left(2x-5\right)\left(x+7\right)=x\left(x+7\right)\)
=>\(\left(2x-5\right)\left(x+7\right)-x\left(x+7\right)=0\)
=>\(\left(x+7\right)\left(2x-5-x\right)=0\)
=>(x+7)(x-5)=0
=>\(\left[{}\begin{matrix}x+7=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-7\\x=5\end{matrix}\right.\)
9: \(\left(3x-2\right)^2-25=0\)
=>\(\left(3x-2-5\right)\left(3x-2+5\right)=0\)
=>\(\left(3x-7\right)\left(3x+3\right)=0\)
=>\(\left[{}\begin{matrix}3x-7=0\\3x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=-1\end{matrix}\right.\)
10: x(3x+5)-6x-10=0
=>x(3x+5)-2(3x+5)=0
=>(3x+5)(x-2)=0
=>\(\left[{}\begin{matrix}3x+5=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{5}{3}\\x=2\end{matrix}\right.\)
11: \(\left(x-1\right)^2+4x-4=0\)
=>\(\left(x-1\right)^2+4\left(x-1\right)=0\)
=>(x-1)(x-1+4)=0
=>(x-1)(x+3)=0
=>\(\left[{}\begin{matrix}x-1=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)
12: \(\left(x-4\right)^2=5x-20\)
=>\(\left(x-4\right)^2=5\left(x-4\right)\)
=>(x-4)(x-4-5)=0
=>(x-4)(x-9)=0
=>\(\left[{}\begin{matrix}x-4=0\\x-9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=9\end{matrix}\right.\)
13: \(\left(2-3x\right)\left(x+11\right)=\left(3x-2\right)\left(2-5x\right)\)
=>\(\left(3x-2\right)\left(x+11\right)=\left(3x-2\right)\left(5x-2\right)\)
=>\(\left(3x-2\right)\left(x+11-5x+2\right)=0\)
=>(3x-2)(-4x+13)=0
=>\(\left[{}\begin{matrix}3x-2=0\\-4x+13=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=\dfrac{13}{4}\end{matrix}\right.\)
14: \(\left(2x-1\right)^2+\left(2-x\right)\left(2x-1\right)=0\)
=>(2x-1)(2x-1+2-x)=0
=>(2x-1)(1-x)=0
=>\(\left[{}\begin{matrix}2x-1=0\\1-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\end{matrix}\right.\)
15: \(2\left(3x+1\right)^2=\left(3x+1\right)\left(x-2\right)\)
=>\(\left(3x+1\right)\left(6x+2\right)-\left(3x+1\right)\left(x-2\right)=0\)
=>\(\left(3x+1\right)\left(6x+2-x+2\right)=0\)
=>\(\left(3x+1\right)\left(5x+4\right)=0\)
=>\(\left[{}\begin{matrix}3x+1=0\\5x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=-\dfrac{4}{5}\end{matrix}\right.\)
16: \(-5\left(4x-1\right)\left(x-2\right)=2\left(4x-1\right)^2\)
=>\(\left(4x-1\right)\left(8x-2\right)+\left(4x-1\right)\left(5x-10\right)=0\)
=>\(\left(4x-1\right)\left(8x-2+5x-10\right)=0\)
=>(4x-1)(13x-12)=0
=>\(\left[{}\begin{matrix}4x-1=0\\13x-12=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=\dfrac{12}{13}\end{matrix}\right.\)
17: \(\left(2x-1\right)\left(5x-7\right)=\left(2x-1\right)\left(9-7x\right)\)
=>\(\left(2x-1\right)\left(5x-7\right)-\left(2x-1\right)\left(9-7x\right)=0\)
=>\(\left(2x-1\right)\left(5x-7-9+7x\right)=0\)
=>(2x-1)(12x-16)=0
=>(3x-4)(2x-1)=0
=>\(\left[{}\begin{matrix}3x-4=0\\2x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=\dfrac{1}{2}\end{matrix}\right.\)
18: \(\left(x-2\right)\left(7-3x\right)=\left(3x-7\right)\left(8x+32\right)\)
=>\(\left(3x-7\right)\left(-x+2\right)-\left(3x-7\right)\left(8x+32\right)=0\)
=>\(\left(3x-7\right)\left(-x+2-8x-32\right)=0\)
=>(3x-7)(-9x-30)=0
=>(3x+10)(3x-7)=0
=>\(\left[{}\begin{matrix}3x+10=0\\3x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{10}{3}\\x=\dfrac{7}{3}\end{matrix}\right.\)
19: \(\left(2-x\right)\left(x+1\right)=\left(x-2\right)\left(3x+5\right)\)
=>\(\left(x-2\right)\left(3x+5\right)-\left(2-x\right)\left(x+1\right)=0\)
=>(x-2)(3x+5)+(x-2)(x+1)=0
=>(x-2)(3x+5+x+1)=0
=>(x-2)(4x+6)=0
=>(2x+3)(x-2)=0
=>\(\left[{}\begin{matrix}2x+3=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=2\end{matrix}\right.\)
20: \(\left(x-1\right)\left(x+7\right)=\left(1-x\right)\left(3-2x\right)\)
=>(x-1)(2x-3)=(x-1)(x+7)
=>(x-1)(2x-3-x-7)=0
=>(x-1)(x-10)=0
=>\(\left[{}\begin{matrix}x-1=0\\x-10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=10\end{matrix}\right.\)
