Why transposing doesn't work (is not working) in quadratic equation?

Question

For example I have an equation:

$4k^2-24k+0=0$

$\implies 4k^2 = 24k$

$\implies 4 × k × k = 24 × k$

$\implies 4k = 24$

$\implies k = 6$

But it doesn't find $0$ as an answer that quadratic equation method or factorisation method does. Why?

Answer 1

Doing the third step ($4k^2 = 24k \implies 4k=24 \ $) you are dividing both sides by k and you can't divide by $0$ so, for this step you are supposing that $k \neq 0$ and you have to check if $k=0$ is a solution.

A better way to solve it is by grouping $4k$, so you get $4k(k-6)=0$ and concluding by this observation: if a product of two real numbers is $0$ then at least one of them must be $0$, so you have $k=0$ and $k=6$ as solutions.