4.a) \(2x^2-10x-3x-2x^2-26=0\)

\(-13x-26=0\Rightarrow-13\left(x+2\right)=0\)

\(\Rightarrow x=-2\)

b) \(2\left(x+5\right)-x^2-5x=0\)

\(2x+10-x^2-5x=0\Leftrightarrow-x^2-3x+10=0\)

\(-\left(x^2+3x-10\right)=0\)

\(-\left(x^2-2x+5x-10\right)=-\left(x\left(x-2\right)+5\left(x-2\right)\right)=0\)

\(-\left(x-2\right)\left(x+5\right)=0\)

\(\left\{{}\begin{matrix}x-2=0\\x+5=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)

c) \(\left(2x-3\right)^2-\left(x+5\right)^2=0\)

\(\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)

\(\left(x-8\right)\left(3x+2\right)=0\)

\(\left\{{}\begin{matrix}x-8=0\\3x+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)

d) \(x^3+x^2-4x-4=0\)

\(x^2\left(x+1\right)-4\left(x+1\right)=0\)

\(\left(x+1\right)\left(x^2-4\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\)

\(\Rightarrow\left\{{}\begin{matrix}x+1=0\\x-2=0\\x+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-1\\x=2\\x=-2\end{matrix}\right.\)

g) \(\left(x-1\right)\left(2x+3-x\right)=0\)

\(\left(x-1\right)\left(x+3\right)=0\)

\(\Rightarrow\left\{{}\begin{matrix}x-1=0\\x+3=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)

h) \(x^2-4x+8-2x+1=x^2-6x+9=0\)

\(\left(x-3\right)^2=0\Rightarrow x=3\)