Question

How do you solve `8k² - 3k =0`?

Answer 1

`k=0"; "k=3/8`

Explanation:

`color(blue)("Determining the first solution")`

Straight away we can observe that if we set `k=0` then it is a
solution to the equation. To emphasise this point:
`8(0^2)-3(0)=0`

This is really the same thing as suggested by mason in that
`8(0^2)-3(0)=0" is equivalent to " k(8k-3)=0` where `k=0`.

`color(blue)("Determining the second solution")`

`8k^2-3x=0`

Also we can write it as:`" "8k^2=3k`

Divide both sides by `k` giving

`8k=3`

`=>k=3/8`

I nearly went on automatic and jump into using the standard formula for resolving `x`. Shows that it is worth taking the time to look hard at the question and see if you can spot any short cuts.