a: x(x-3)-7x+21=0
=>x(x-3)-7(x-3)=0
=>(x-3)(x-7)=0
=>\(\left[{}\begin{matrix}x-3=0\\x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=7\end{matrix}\right.\)
b: \(2x\left(x+3\right)+\left(2x+3\right)\left(5-x\right)=0\)
=>\(2x^2+6x+10x-2x^2+15-3x=0\)
=>13x+15=0
=>\(x=-\dfrac{15}{13}\)
c: \(2x\left(x-5\right)-x\left(2x+3\right)=26\)
=>\(2x^2-10x-2x^2-3x=26\)
=>-13x=26
=>x=-2
d: \(\left(x+3\right)\left(x+4\right)-\left(x-3\right)\left(x-5\right)=2\)
=>\(x^2+4x+3x+12-\left(x^2-3x-5x+15\right)=2\)
=>\(x^2+7x+12-x^2+8x-15=2\)
=>15x-3=2
=>15x=5
=>\(x=\dfrac{1}{3}\)
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