Question

How do you solve `(2x-1)(x+3)=0`?

Answer 1

`x=1/2" or "x=-3`

Explanation:

For this equation to become the value of zero it means that either the left bracket is zero or the right bracket is zero.

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Consider `color(blue)((2x-1)=0)`

`color(magenta)("Detailed calculation to show how it works")`

Add `color(red)( 1)` to both sides

`" "color(blue)(2x-1color(red)(+1)=0color(red)(+1))`

`" "color(blue)(2x+0=1)`

Divide both sides by `color(red)(2)`

`" "color(blue)(2/(color(red)(2))xx x=1/(color(red)(2))`

But `2/2 = 1` giving

`x=1/2`

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Consider `color(blue)((x+3)=0)`

`color(magenta)("Calculation skipping steps")`

`x=-3`
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Answer 2

`x` can equal `-1/2` or `-3`

Explanation:

`(2x-1)(x+3)=0`

To solve for the value of `x` simply take each of the binomial factors and set them equal to zero.

`2x+1 = 0`
`2xcancel(+1)cancel-1 = 0-1`
`(cancel2x)/cancel2 =-1/2`
`x=-1/2`

`x+3 = 0`
`xcancel(+3)cancel-3 = 0-3`
`x=-3`

`x` can equal `-1/2` or `-3`