Step by step
The question
Question: solve x² − x − 12 = 0.
1 Factor
We need two numbers.
They multiply to −12, and they add to −1.
They multiply to a minus number, so one number is plus and one is minus.
They add to a minus number, so the bigger one is minus.
We list the pairs that make 12, smallest first.
We take the smaller from the bigger.
We need 1.
3 and 4 give 1.
Yes!
With the signs: 3 and −4.
So it is (x + 3)(x − 4) = 0.
2 One bracket is 0
Two numbers multiply to 0.
That only happens if one of them is 0.
So one bracket must be 0.
We make each bracket 0.
Two small equations.
In x + 3 = 0, we take away 3 on both sides.
In x − 4 = 0, we add 4 on both sides.
So x = −3 or x = 4.
3 Check
Let's check: put x = −3 into the left side.
We get 0, the same as the right side.
It works!
Now put x = 4 into the left side.
We get 0 again, the same as the right side.
So both answers are right!
Let's look back.
First: factor.
Then: one bracket is 0.
Last: check.