Step by step
The question
Question: solve x² + 5x + 6 = 0.
There is an x².
1 Factor
Factoring goes backwards.
We need two numbers.
They multiply to 6, and they add to 5.
Look at the sign in front of 6: it is plus.
So the two numbers have the same sign.
Now the sign in front of 5x: it is plus.
So both are plus.
We list the pairs that make 6, smallest first.
For each pair, we check two things: they multiply to 6, and they add to 5.
1 × 6 = 6.
1 + 6 = 7.
Not 5.
2 × 3 = 6.
2 + 3 = 5.
Both work!
So the two numbers are 2 and 3.
So it is (x + 2)(x + 3) = 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 + 2 = 0, we take away 2 on both sides.
In x + 3 = 0, we take away 3 on both sides.
So x = −2 or x = −3.
3 Check
Let's check: put x = −2 into the left side.
We get 0, the same as the right side.
It works!
Now put x = −3 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.