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