Solve the following quadratic equations by factorization:

We have been given

$x^{2}+2 a b=(2 a+b) x$

$x^{2}-(2 a+b) x+2 a b=0$

$x^{2}-2 a x-b x+2 a b=0$

$x(x-2 a)-b(x-2 a)=0$

$(x-2 a)(x-b)=0$

Therefore,

$x-2 a=0$

$x=2 a$

or,

$x-b=0$

$x=b$

Hence, $x=2 a$ or $x=b$.