Question

How do you solve the equation for `x^2 - 3x = 0`?

Answer 1

`x^2 - 3x = 0`

`x*(x-3) = 0` (`x` was a common factor to both the terms)

In general, if `a*b = 0,` then either `a = 0 or b = 0`

So here,
`x = 0 or x - 3 = 0`
`color(green)( x = 0 or x = 3` is the correct Solution.

`color(red)(Note` :

Here's a classic `color(red)(Mistake` that many students make:

Transpose `3x` to the right hand side

`x^2 = 3x`

Divide both sides by `x` will give us `x = 3` (Incorrect/Incomplete)

This is a `color(red)(mistake` because we CANNOT divide by `x` unless we are sure about it not being equal to zero.

Answer 2

To find `x`, we first have to factorize the equation.
`x^2-3x=0`
As `x` is the common factor between the 2 values, we factorize the equation by taking `x` out of `x^2-3x=0`

`x^2-3x=0`
`x(x-3)=0`

Any value that is multiplied by 0, will give 0 as the answer.
1x0=0
2x0=0
3x0=0

From here, we know that in `x(x-3)=0`,
`x=0` and `(x-3)=0`

`(x-3)=0`
`x=3`

Therefore `x=0` and `x=3`