Question

How do you solve `(2x + 1)(x - 4) = -7`?

Answer 1

Given `color(red)((2x+1))color(blue)((x-4)) = color(orange)(-7)`

Multiply the two terms on the left side
(for demonstration purposes I used the distributive property, but there are several ways to do this)
`color(red)(2x)color(blue)((x-4)) + color(red)(1)color(blue)((x-4)) = color(orange)(-7)`

`2x^2 -8x + x -4 = color(orange)(-7)`

`2x^2-7x-4 = color(orange)(-7)`

Rearrange all non-zero terms to the left-side
`2x^2-7x+3 = 0`

Factor the left side
`(2x-1)(x-3) = 0`

State the solutions:
`x= 1/2` or `x= 3`