Question

How do you solve `(x + 3) ( x - 1) = 32`?

Answer 1

`x=-7,5`

Explanation:

Solve:

`(x+3)(x-1)=32`

FOIL the left-hand side.
https://www.mathsisfun.com/definitions/foil-method.html

`x^2+2x-3=32`

Move all terms to the left-hand side.

`x^2+2x-3-32=0`

`x^2+2x-35=0`

Find two numbers that when added equal `2` and when multiplied equal `-35`. The numbers `7` and `-5` meet the criteria.

`(x+7)(x-5)+0`

`x+7=0`

`x=-7`

`x-5=0`

`x=5`

`x=-7,5`

Answer 2

First of all, you do the multiplications, so you get:
`x^2+2x-3=32`
Then you put the 32 on the first class just like:
`x^2+2x-35=0`
Then you do `D=2^2-4*(-35) = 144` (Using the method `D = b^2-4ac`)
so your one root is `x_1=(b-sqrt(D))/(2a)`
and the other one is `x_2=(b+sqrt(D))/(2a)`
Do the maths and you get `x_1=-7` , `x_2=5`