\(5.\left(x-3\right)\left(x+3\right)=\left(x-5\right)^2\\ \Leftrightarrow x^2-9=x^2-10x+9\\ \Leftrightarrow-10x+9=-9\\ \Leftrightarrow-10x=-18\\ \Leftrightarrow x=-\dfrac{18}{-10}=\dfrac{9}{5}\\ 6.\left(2x+1\right)^2-4x\left(x-1\right)=17\\ \Leftrightarrow\left(4x^2+4x+1\right)-4x\left(x-1\right)=17\\ \Leftrightarrow4x^2+4x+1-4x^2+4x=17\\ \Leftrightarrow8x+1=17\\ \Leftrightarrow8x=17-1=16\\ \Leftrightarrow x=\dfrac{16}{8}=2\\ 7.\left(3x+1\right)^2-9x\left(x-2\right)=25\\ \Leftrightarrow9x^2+6x+1-9x^2+18x=25\\ \Leftrightarrow24x+1=25\\ \Leftrightarrow24x=25-1=24\\ \Leftrightarrow x=\dfrac{24}{24}=1\\ 8.\left(3x-2\right)\left(3x+2\right)-9\left(x-1\right)x=0\\ \Leftrightarrow\left(9x^2-4\right)-9x\left(x-1\right)=0\\ \Leftrightarrow9x^2-4-9x^2+9x=0\\ \Leftrightarrow9x-4=0\\ \Leftrightarrow9x=4\\ \Leftrightarrow x=\dfrac{4}{9}\)
9: \(\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\)
=>\(\left(x+2\right)\left(x+2-x+2\right)=0\)
=>4(x+2)=0
=>x+2=0
=>x=-2
10: \(\left(x+2\right)^2-\left(x-3\right)\left(x+3\right)=-3\)
=>\(x^2+4x+4-x^2+9=-3\)
=>4x+13=-3
=>4x=-16
=>x=-4
11: \(\left(3x+2\right)^2-\left(3x-5\right)\left(3x+2\right)=0\)
=>\(\left(3x+2\right)\left(3x+2-3x+5\right)=0\)
=>7(3x+2)=0
=>3x+2=0
=>\(x=-\dfrac{2}{3}\)
12: \(\left(x+3\right)^2-\left(x+2\right)\left(x-2\right)=4x+17\)
=>\(x^2+6x+9-x^2+4=4x+17\)
=>6x+13=4x+17
=>2x=4
=>x=2
13: \(3\left(x-1\right)^2+\left(x+5\right)\left(2-3x\right)=-25\)
=>\(3\left(x^2-2x+1\right)+2x-3x^2+10-15x=-25\)
=>\(3x^2-6x+3-3x^2-13x+10+25=0\)
=>-19x=-38
=>x=2
14:
\(\left(x+3\right)^2+\left(x-2\right)^2=2x^2\)
=>\(x^2+6x+9+x^2-4x+4=2x^2\)
=>2x+13=0
=>2x=-13
=>\(x=-\dfrac{13}{2}\)
