Step by step
The question
Question: solve x² − 4x = 0.
x2 − 4x = 0
1 Factor
There is no plain number.
Both parts have x in them.
So we take x out.
x² = x × x, −4x = x × (−4)
So it is x(x − 4) = 0.
x(x − 4) = 0
Careful!
Don't divide both sides by x.
Then the answer x = 0 would be lost.
Careful: don't divide by x. We would lose x = 0.
2 One bracket is 0
x times the bracket is 0.
That only happens if one of them is 0.
A × B = 0 → A = 0 or B = 0
We make each part 0.
Two small equations.
x = 0 or x − 4 = 0
x = 0 is done already.
In x − 4 = 0, we add 4 on both sides.
x = 0 or x − 4 + 4 = 0 + 4
So x = 0 or x = 4.
x = 0 or x = 4
3 Check
Let's check: put x = 0 into the left side.
x = 0: 02 − 4(0) = 0 + 0 = 0
We get 0, the same as the right side.
It works!
Now put x = 4 into the left side.
x = 4: 42 − 4(4) = 16 − 16 = 0
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.
Answer
x = 0 or x = 4