Question

How do you solve `3(4 - x)(2x + 1) = 0`?

Answer 1

See a solution process below:

Explanation:

First, divide each side of the equation by `color(red)(3)` to eliminate the constant while keeping the equation balanced"

`(3(4 - x)(2x + 1))/color(red)(3) = 0/color(red)(3)`

`(color(red)(cancel(color(black)(3)))(4 - x)(2x + 1))/cancel(color(red)(3)) = 0`

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

Solve each term on the left side of the equation for `0`:

Solution 1)

`4 - x = 0`

`-color(red)(4) + 4 - x = -color(red)(4) + 0`

`0 - x = -4`

`-x = -4`

`color(red)(-1) xx -x = color(red)(-1) xx -4`

`x = 4`

Solution 2)

`2x + 1 = 0`

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

`2x + 0 = -1`

`2x = -1`

`(2x)/color(red)(2) = -1/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -1/2`

`x = -1/2`

The solutions are: `x = 4` and `x = -1/2`